Subjects -> MATHEMATICS (Total: 1082 journals)
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    - MATHEMATICS (800 journals)
    - MATHEMATICS (GENERAL) (43 journals)
    - NUMERICAL ANALYSIS (24 journals)
    - PROBABILITIES AND MATH STATISTICS (106 journals)

MATHEMATICS (800 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 5)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 4)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 7)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 16)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 3)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Hybrid Journal   (Followers: 39)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 12)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 2)
Acta Mathematica Scientia     Full-text available via subscription   (Followers: 5)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 6)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 12)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 4)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 6)
Advances in Catalysis     Full-text available via subscription   (Followers: 5)
Advances in Complex Systems     Hybrid Journal   (Followers: 10)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 23)
Advances in Decision Sciences     Open Access   (Followers: 4)
Advances in Difference Equations     Open Access   (Followers: 3)
Advances in Fixed Point Theory     Open Access   (Followers: 8)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 19)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 11)
Advances in Materials Science     Open Access   (Followers: 19)
Advances in Mathematical Physics     Open Access   (Followers: 8)
Advances in Mathematics     Full-text available via subscription   (Followers: 17)
Advances in Nonlinear Analysis     Open Access   (Followers: 1)
Advances in Numerical Analysis     Open Access   (Followers: 9)
Advances in Operations Research     Open Access   (Followers: 13)
Advances in Operator Theory     Hybrid Journal   (Followers: 2)
Advances in Porous Media     Full-text available via subscription   (Followers: 5)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 10)
Advances in Pure Mathematics     Open Access   (Followers: 10)
Advances in Science and Research (ASR)     Open Access   (Followers: 9)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 9)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 7)
Afrika Matematika     Hybrid Journal   (Followers: 3)
Air, Soil & Water Research     Open Access   (Followers: 13)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 3)
AKSIOMATIK : Jurnal Penelitian Pendidikan dan Pembelajaran Matematika     Open Access  
Al-Jabar : Jurnal Pendidikan Matematika     Open Access   (Followers: 1)
Al-Qadisiyah Journal for Computer Science and Mathematics     Open Access   (Followers: 1)
AL-Rafidain Journal of Computer Sciences and Mathematics     Open Access   (Followers: 6)
Algebra and Logic     Hybrid Journal   (Followers: 7)
Algebra Colloquium     Hybrid Journal   (Followers: 4)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Open Access   (Followers: 5)
Algorithms     Open Access   (Followers: 12)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 10)
American Journal of Mathematical Analysis     Open Access   (Followers: 2)
American Journal of Mathematical and Management Sciences     Hybrid Journal   (Followers: 1)
American Journal of Mathematics     Full-text available via subscription   (Followers: 7)
American Journal of Operations Research     Open Access   (Followers: 8)
American Mathematical Monthly     Full-text available via subscription   (Followers: 6)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 11)
Anadol University Journal of Science and Technology B : Theoritical Sciences     Open Access  
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access  
Analysis and Applications     Hybrid Journal   (Followers: 1)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 6)
Analysis Mathematica     Full-text available via subscription  
Analysis. International mathematical journal of analysis and its applications     Hybrid Journal   (Followers: 5)
Annales Mathematicae Silesianae     Open Access   (Followers: 2)
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica     Open Access   (Followers: 1)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica     Open Access  
Annali di Matematica Pura ed Applicata     Hybrid Journal   (Followers: 1)
Annals of Combinatorics     Hybrid Journal   (Followers: 4)
Annals of Data Science     Hybrid Journal   (Followers: 13)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 8)
Annals of Functional Analysis     Hybrid Journal   (Followers: 1)
Annals of Mathematics     Full-text available via subscription   (Followers: 2)
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 14)
Annals of PDE     Hybrid Journal  
Annals of Pure and Applied Logic     Open Access   (Followers: 4)
Annals of the Alexandru Ioan Cuza University - Mathematics     Open Access  
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1)
Annals of West University of Timisoara - Mathematics     Open Access  
Annals of West University of Timisoara - Mathematics and Computer Science     Open Access   (Followers: 2)
Annuaire du Collège de France     Open Access   (Followers: 6)
ANZIAM Journal     Open Access   (Followers: 1)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 3)
Applications of Mathematics     Hybrid Journal   (Followers: 3)
Applied Categorical Structures     Hybrid Journal   (Followers: 4)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 14)
Applied Mathematics     Open Access   (Followers: 4)
Applied Mathematics     Open Access   (Followers: 8)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 10)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal   (Followers: 1)
Applied Mathematics and Nonlinear Sciences     Open Access  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 4)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Network Science     Open Access   (Followers: 3)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 6)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 4)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 3)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 6)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 6)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
Armenian Journal of Mathematics     Open Access   (Followers: 1)
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites     Open Access   (Followers: 25)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian Research Journal of Mathematics     Open Access   (Followers: 1)
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 3)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 7)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 5)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 2)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access   (Followers: 1)
Baltic International Yearbook of Cognition, Logic and Communication     Open Access   (Followers: 2)
Banach Journal of Mathematical Analysis     Hybrid Journal   (Followers: 1)
Basin Research     Hybrid Journal   (Followers: 5)
BIBECHANA     Open Access   (Followers: 2)
Biomath     Open Access  
BIT Numerical Mathematics     Hybrid Journal   (Followers: 1)
Boletim Cearense de Educação e História da Matemática     Open Access  
Boletim de Educação Matemática     Open Access  
Boletín de la Sociedad Matemática Mexicana     Hybrid Journal  
Bollettino dell'Unione Matematica Italiana     Full-text available via subscription   (Followers: 2)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 19)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 13)
Bulletin des Sciences Mathamatiques     Full-text available via subscription   (Followers: 4)
Bulletin of Dnipropetrovsk University. Series : Communications in Mathematical Modeling and Differential Equations Theory     Open Access   (Followers: 3)
Bulletin of Mathematical Sciences     Open Access   (Followers: 1)
Bulletin of Symbolic Logic     Full-text available via subscription   (Followers: 2)
Bulletin of the Australian Mathematical Society     Full-text available via subscription   (Followers: 2)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the Iranian Mathematical Society     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 3)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Cadernos do IME : Série Matemática     Open Access   (Followers: 1)
Calculus of Variations and Partial Differential Equations     Hybrid Journal  
Canadian Journal of Mathematics / Journal canadien de mathématiques     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 22)
Canadian Mathematical Bulletin     Hybrid Journal  
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CEAS Space Journal     Hybrid Journal   (Followers: 2)
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 3)
Chaos, Solitons & Fractals : X     Open Access  
ChemSusChem     Hybrid Journal   (Followers: 8)
Chinese Annals of Mathematics, Series B     Hybrid Journal  
Chinese Journal of Catalysis     Full-text available via subscription   (Followers: 2)
Chinese Journal of Mathematics     Open Access  
Ciencia     Open Access   (Followers: 1)
Clean Air Journal     Full-text available via subscription   (Followers: 1)
CODEE Journal     Open Access   (Followers: 2)
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 3)
Collectanea Mathematica     Hybrid Journal  
College Mathematics Journal     Hybrid Journal   (Followers: 4)
COMBINATORICA     Hybrid Journal  
Combinatorics, Probability and Computing     Hybrid Journal   (Followers: 4)
Combustion Theory and Modelling     Hybrid Journal   (Followers: 15)
Commentarii Mathematici Helvetici     Hybrid Journal  
Communications in Advanced Mathematical Sciences     Open Access  
Communications in Combinatorics and Optimization     Open Access  
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 4)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 4)
Complex Analysis and its Synergies     Open Access   (Followers: 3)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Composite Materials Series     Full-text available via subscription   (Followers: 9)
Compositio Mathematica     Full-text available via subscription  
Comptes Rendus Mathematique     Full-text available via subscription  
Computational and Applied Mathematics     Hybrid Journal   (Followers: 4)
Computational and Mathematical Methods     Hybrid Journal  
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 2)
Computational Complexity     Hybrid Journal   (Followers: 4)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 9)
Computational Mechanics     Hybrid Journal   (Followers: 5)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 9)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 11)
Concrete Operators     Open Access   (Followers: 4)
Confluentes Mathematici     Hybrid Journal  
Contributions to Game Theory and Management     Open Access  
COSMOS     Hybrid Journal  
Cryptography and Communications     Hybrid Journal   (Followers: 13)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Current Research in Biostatistics     Open Access   (Followers: 8)
Czechoslovak Mathematical Journal     Hybrid Journal   (Followers: 1)
Demographic Research     Open Access   (Followers: 15)
Demonstratio Mathematica     Open Access  
Dependence Modeling     Open Access  
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 31)
Desimal : Jurnal Matematika     Open Access   (Followers: 2)

        1 2 3 4 | Last

Similar Journals
Journal Cover
Advances in Computational Mathematics
Journal Prestige (SJR): 0.812
Citation Impact (citeScore): 1
Number of Followers: 23  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1572-9044 - ISSN (Online) 1019-7168
Published by Springer-Verlag Homepage  [2626 journals]
  • A cubic spline penalty for sparse approximation under tight frame balanced
           model
    • Abstract: Abstract The study of non-convex penalties has recently received considerable attentions in sparse approximation. The existing non-convex penalties are proposed on the principle of seeking for a continuous alternative to the ℓ0-norm penalty. In this paper, we come up with a cubic spline penalty (CSP) which is also continuous but closer to ℓ0-norm penalty compared to the existing ones. As a result, it produces the weakest bias among them. Wavelet tight frames are efficient for sparse approximation due to its redundancy and fast implementation algorithm. We adopt a tight frame balanced model with our proposed cubic spline penalty since the balanced model takes the advantages of both analysis and synthesis model. To solve the non-convex CSP penalized problem, we employ a proximal local linear approximation (PLLA) algorithm and prove the generated sequence converges to a stationary point of the model if it is bounded. Under additional conditions, we find that the limit point behaves as well as the oracle solution, which is obtained by using the exact support of the ground truth signal. The efficiency of our cubic spline penalty are further demonstrated in applications of variable selection and image deblurring.
      PubDate: 2020-04-02
       
  • Structured backward error analysis for generalized saddle point problems
    • Abstract: Abstract Recently, the structured backward errors for the generalized saddle point problems with some different structures have been studied by some authors, but their results involve some Kronecker products, the vec-permutation matrices, and the orthogonal projection of a large block matrix which make them very expensive to compute when utilized for testing the stability of a practical algorithm or as an effective stopping criteria. In this paper, adopting a new technique, we present the explicit and computable formulae of the normwise structured backward errors for the generalized saddle point problems with five different structures. Our analysis can be viewed as a unified or general treatment for the structured backward errors for all kinds of saddle point problems and the derived results also can be seen as the generalizations of the existing ones for standard saddle point problems, including some Karush-Kuhn-Tucker systems. Some numerical experiments are performed to illustrate that our results can be easily used to test the stability of practical algorithms when applied some physical problems. We also show that the normwise structured and unstructured backward errors can be arbitrarily far apart in some certain cases.
      PubDate: 2020-04-02
       
  • A robust second-order surface reconstruction for shallow water flows with
           a discontinuous topography and a Manning friction
    • Abstract: Abstract A second-order surface reconstruction (SR) method for the shallow water equations with a discontinuous bottom topography and a Manning friction source term is presented. We redefine the water surface level at the cell interface by using the minimum difference between the bottom level and the original water surface level. The reconstructed water surface level is used to define the intermediate bottom level and the intermediate water height at the cell interface. We propose an explicit-implicit method to address the friction source term. The new second-order SR scheme together with the explicit-implicit method can preserve a special steady-state solution of the system and can maintain the positivity of the water depth. We also extend the new scheme to two-dimensional shallow water flows. To demonstrate the robustness and effectiveness of the new scheme, we use several classical numerical experiments for the shallow water flows over a complex bottom topography.
      PubDate: 2020-04-02
       
  • Exponential boundary-layer approximation space for solving the
           compressible laminar Navier-Stokes equations
    • Abstract: Abstract In general, it needs to take about nearly 10 grid points inside a wall boundary layer for low accuracy order methods to get satisfactory wall-normal gradient related results, such as friction coefficient and wall heat flux. If there exist extreme points inside the boundary layer, this situation becomes even worse. In this work, with the help of the analytic solution of the one-dimensional steady compressible Navier-Stokes equations under some restrictions, we show that the flow variables actually vary in the form of an exponential function instead of a polynomial one inside the boundary layer. Then, we propose an exponential space for approximating the solutions inside the boundary layer and numerically implementing it in the frame of direct discontinuous Galerkin (DDG) method. We show that the DDG methods based on the exponential boundary-layer space give much better numerical results for both conservative variables and wall-normal gradients than those with the standard polynomial space. Generally only 1–2 grid points inside the boundary layer are demanded to resolve the wall boundary layer to obtain satisfactory wall-normal gradients under the exponential space. Preliminary extension to two-dimensional laminar boundary-layer flow shows a similar performance of the proposed exponential boundary-layer space, exhibiting its potential applications in high dimensions.
      PubDate: 2020-03-30
       
  • An efficient method for non-negative low-rank completion
    • Abstract: Abstract In this article, we propose a new method for low-rank completion of a large sparse matrix, subject to non-negativity constraint. As a challenging prototype of this problem, we have in mind the well-known Netflix problem. Our method is based on the derivation of a constrained gradient system and its numerical integration. The methods we propose are based on the constrained minimization of a functional associated to the low-rank completion matrix having minimal distance to the given matrix. In the main 2-level method, the low-rank matrix is expressed in the form of the non-negative factorization X = εUVT, where the factors U and V are assumed to be normalized with unit Frobenius norm. In the inner level—for a given ε—we minimize the functional; in the outer level, we tune the parameter ε until we reach a solution. Numerical experiments on well-known large test matrices show the effectiveness of the method when compared with other algorithms available in the literature.
      PubDate: 2020-03-23
       
  • Rigorous and effective a-posteriori error bounds for nonlinear
           problems—application to RB methods
    • Abstract: Abstract Quantifying the error that is induced by numerical approximation techniques is an important task in many fields of applied mathematics. Two characteristic properties of error bounds that are desirable are reliability and efficiency. In this article, we present an error estimation procedure for general nonlinear problems and, in particular, for parameter-dependent problems. With the presented auxiliary linear problem (ALP)-based error bounds and corresponding theoretical results, we can prove large improvements in the accuracy of the error predictions compared with existing error bounds. The application of the procedure in parametric model order reduction setting provides a particularly interesting setup, which is why we focus on the application in the reduced basis framework. Several numerical examples illustrate the performance and accuracy of the proposed method.
      PubDate: 2020-03-23
       
  • Vector versions of Prony’s algorithm and vector-valued rational
           approximations
    • Abstract: Abstract Given the scalar sequence \(\{f_{m}\}^{\infty }_{m=0}\) that satisfies $$ f_{m} = \sum\limits_{i=1}^{k} {a_{i}}{\zeta}_{i}^{m},\quad m=0,1,\ldots, $$ where \(a_{i}, \zeta _{i}\in \mathbb {C}\) and ζi are distinct, the algorithm of Prony concerns the determination of the ai and the ζi from a finite number of the fm. This algorithm is also related to Padé approximants from the infinite power series \({\sum }^{\infty }_{j=0}f_{j}z^{j}\). In this work, we discuss ways of extending Prony’s algorithm to sequences of vectors \({\{\boldsymbol {f}_{m}\}}^{\infty }_{m=0}\) in \(\mathbb {C}^{N}\) that satisfy $$ \boldsymbol{f}_{m} = \sum\limits_{i=1}^{k} \boldsymbol{a}_{i} {\zeta}_{i}^{m}, \quad m=0,1,\ldots, $$ where \(\boldsymbol {a}_{i}\in \mathbb {C}^{N}\) and \(\zeta _{i}\in \mathbb {C}\). Two distinct problems arise depending on whether the vectors ai are linearly independent or not. We consider different approaches that enable us to determine the ai and ζi for these two problems, and develop suitable methods. We concentrate especially on extensions that take into account the possibility of the components of the ai being coupled. One of the applications we consider concerns the case in which $$ \boldsymbol{f}_{m} = \sum\limits_{i=1}^{r} \boldsymbol{a}_{i} {\zeta}_{i}^{m}, \quad m=0,1,\ldots,\quad r \text{ large}, $$ and we would like to approximate/determine of a number of the pairs (ζi, ai) for which ζi are largest. We present the related theory and provide numerical examples that confirm this theory. This application can be extended to the more general case in which $$ \boldsymbol{f}_{m} = \sum\limits_{i=1}^{r} \boldsymbol{p}_{i} (m){\zeta}_{i}^{m}, \quad m=0,1,\ldots, $$ where \(\boldsymbol {p}_{i}(m)\in \mathbb {C}^{N}\) are some (vector-valued) polynomials in m, and \(\zeta _{i}\in \mathbb {C}\) are distinct. Finally, the methods suggested here can be extended to vector sequences in infinite dimensional spaces in a straightforward manner.
      PubDate: 2020-03-19
       
  • Lévy-driven stochastic Volterra integral equations with doubly singular
           kernels: existence, uniqueness, and a fast EM method
    • Abstract: Abstract This paper considers Lévy noise driven nonlinear stochastic Volterra integral equations with doubly weakly singular kernels, whose singular points include both s = 0 and s = t. The existence and uniqueness theorem of the true solution as well as the strong convergence rate of the Euler–Maruyama (EM) method are developed via establishing some fine estimates. Compared with the corresponding results by Wang (Statist Probab Lett 78: 1062–1071, 2008) and Zhang (J Differential Equations 244: 2226–2250, 2008), our results generalize the Gaussian noise case to the Lévy noise case, relax the integrable limitations of singular kernels and establish an accurate convergence order. Moreover, based on the efficient sum-of-exponentials approximation, a fast EM method is presented to improve the low computational efficiency of the EM method. Specifically, when T ≫ 1, the computational complexity O(N2) and the storage O(N) of the EM method are reduced to \(O(N\log N)\) and \(O(\log N)\) respectively; while T ≈ 1, they are reduced to \(O(N\log ^{2} N)\) and \(O(\log ^{2} N)\) respectively, where T and N denote the terminal time and the total number of time steps respectively. Finally, the numerical example supports the theoretical results and explains the priority of the fast EM method.
      PubDate: 2020-03-18
       
  • Characterization and extensive study of cubic and quintic algebraic
           trigonometric planar PH curves
    • Abstract: Abstract This paper deals with Pythagorean hodograph curves of the spaces of algebraic trigonometric functions and trigonometric polynomials, \(\text {span}\left \{1,t,\left \{{\cos \limits } \left ({kt}\right ), {\sin \limits } \left ({kt}\right )\right \}_{k=1}^{m}\right \} \) and \( \text {span}\left \{1,\left \{{\cos \limits } \left ({kt}\right ), {\sin \limits } \left ({kt}\right )\right \}_{k=1}^{m}\right \}, \) respectively. First, we propose a general characterization of planar PH curves in these spaces. Next, we consider the particular cases m = 1 and m = 2. For each of them, we give the general form of the control polygon of the PH curves, the implicit relations defining these curves, and their geometrical interpretations. Some examples and particular cases complete this study.
      PubDate: 2020-03-16
       
  • Drift-preserving numerical integrators for stochastic Hamiltonian systems
    • Abstract: Abstract The paper deals with numerical discretizations of separable nonlinear Hamiltonian systems with additive noise. For such problems, the expected value of the total energy, along the exact solution, drifts linearly with time. We present and analyze a time integrator having the same property for all times. Furthermore, strong and weak convergence of the numerical scheme along with efficient multilevel Monte Carlo estimators are studied. Finally, extensive numerical experiments illustrate the performance of the proposed numerical scheme.
      PubDate: 2020-03-16
       
  • Discontinuous finite volume element method for a coupled
           Navier-Stokes-Cahn-Hilliard phase field model
    • Abstract: Abstract In this paper, we propose a discontinuous finite volume element method to solve a phase field model for two immiscible incompressible fluids. In this finite volume element scheme, discontinuous linear finite element basis functions are used to approximate the velocity, phase function, and chemical potential while piecewise constants are used to approximate the pressure. This numerical method is efficient, optimally convergent, conserving the mass, convenient to implement, flexible for mesh refinement, and easy to handle complex geometries with different types of boundary conditions. We rigorously prove the mass conservation property and the discrete energy dissipation for the proposed fully discrete discontinuous finite volume element scheme. Using numerical tests, we verify the accuracy, confirm the mass conservation and the energy law, test the influence of surface tension and small density variations, and simulate the driven cavity, the Rayleigh-Taylor instability.
      PubDate: 2020-03-14
       
  • A conservative sine pseudo-spectral-difference method for
           multi-dimensional coupled Gross–Pitaevskii equations
    • Abstract: Abstract In this paper, a sine pseudo-spectral-difference scheme that preserves the discrete mass and energy is presented and analyzed for the coupled Gross–Pitaevskii equations with Dirichlet boundary conditions in several spatial dimensions. The Crank–Nicolson finite difference method is employed for approximating the time derivative, and the second-order sine spectral differentiation matrix is deduced and applied in spatial discretization. Without any restrictions on the grid ratios, optimal error estimates are established by utilizing the discrete energy method and the equivalence of (semi-)norms. An accelerated algorithm is developed to speed up the numerical implementation with the help of fast sine transform. Numerical examples are tested to confirm the effectiveness and high accuracy of the method.
      PubDate: 2020-03-14
       
  • Two-grid Raviart-Thomas mixed finite element methods combined with
           Crank-Nicolson scheme for a class of nonlinear parabolic equations
    • Abstract: Abstract In this paper, we discuss a priori error estimates of two-grid mixed finite element methods for a class of nonlinear parabolic equations. The lowest order Raviart-Thomas mixed finite element and Crank-Nicolson scheme are used for the spatial and temporal discretization. First, we derive the optimal a priori error estimates for all variables. Second, we present a two-grid scheme and analyze its convergence. It is shown that if the two mesh sizes satisfy h = H2, then the two-grid method achieves the same convergence property as the Raviart-Thomas mixed finite element method. Finally, we give a numerical example to verify the theoretical results.
      PubDate: 2020-03-10
       
  • A linearly implicit structure-preserving Fourier pseudo-spectral scheme
           for the damped nonlinear Schrödinger equation in three dimensions
    • Abstract: Abstract In this paper, we propose a linearly implicit Fourier pseudo-spectral scheme, which preserves the total mass and energy conservation laws for the damped nonlinear Schrödinger equation in three dimensions. With the aid of the semi-norm equivalence between the Fourier pseudo-spectral method and the finite difference method, an optimal L2-error estimate for the proposed method without any restriction on the grid ratio is established by analyzing the real and imaginary parts of the error function. Numerical results are addressed to confirm our theoretical analysis.
      PubDate: 2020-03-09
       
  • Optimal frame designs for multitasking devices with weight restrictions
    • Abstract: Abstract Let \(\mathbf d=(d_{j})_{j\in \mathbb {I}_{m}}\in \mathbb {N}^{m}\) be a finite sequence (of dimensions) and \(\alpha =(\alpha _{i})_{i\in \mathbb {I}_{n}}\) be a sequence of positive numbers (of weights), where \(\mathbb {I}_{k}=\{1,\ldots ,k\}\) for \(k\in \mathbb {N}\). We introduce the (α, d)-designs, i.e., m-tuples \({\Phi }=(\mathcal F_{j})_{j\in \mathbb {I}_{m}}\) such that \(\mathcal F_{j}=\{f_{ij}\}_{i\in \mathbb {I}_{n}}\) is a finite sequence in \(\mathbb {C}^{d_{j}}\), \(j\in \mathbb {I}_{m}\), and such that the sequence of non-negative numbers \((\ f_{ij}\ ^{2})_{j\in \mathbb {I}_{m}}\) forms a partition of αi, \(i\in \mathbb {I}_{n}\). We characterize the existence of (α, d)-designs with prescribed properties in terms of majorization relations. We show, by means of a finite step algorithm, that there exist (α, d)-designs \({\Phi }^{\text {op}}=(\mathcal {F}_{j}^{\text {op}})_{j\in \mathbb {I}_{m}}\) that are universally optimal; that is, for every convex function \(\varphi :[0,\infty )\rightarrow [0,\infty )\), then Φop minimizes the joint convex potential induced by φ among (α, d)-designs, namely $ \sum \limits_{j\in \mathbb I_{m}}\text {P}_{\varphi }(\mathcal F_{j}^{\text {op}})\leq \sum \limits_{j\in \mathbb I_{m}}\text {P}_{\varphi }(\mathcal F_{j}) $ for every (α, d)-design \({\Phi }=(\mathcal F_{j})_{j\in \mathbb {I}_{m}}\), where \(\text {P}_{\varphi }(\mathcal F)=\text {tr}(\varphi (S_{\mathcal {F}}))\); in particular, Φop minimizes both the joint frame potential and the joint mean square error among (α, d)-designs. We show that in this case, \(\mathcal {F}_{j}^{\text {op}}\) is a frame for \(\mathbb {C}^{d_{j}}\), for \(j\in \mathbb {I}_{m}\). This corresponds to the existence of optimal encoding-decoding schemes for multitasking devices with energy restrictions.
      PubDate: 2020-03-07
       
  • Worst-case optimal approximation with increasingly flat Gaussian kernels
    • Abstract: Abstract We study worst-case optimal approximation of positive linear functionals in reproducing kernel Hilbert spaces induced by increasingly flat Gaussian kernels. This provides a new perspective and some generalisations to the problem of interpolation with increasingly flat radial basis functions. When the evaluation points are fixed and unisolvent, we show that the worst-case optimal method converges to a polynomial method. In an additional one-dimensional extension, we allow also the points to be selected optimally and show that in this case convergence is to the unique Gaussian quadrature–type method that achieves the maximal polynomial degree of exactness. The proofs are based on an explicit characterisation of the reproducing kernel Hilbert space of the Gaussian kernel in terms of exponentially damped polynomials.
      PubDate: 2020-03-06
       
  • A boundary integral equation approach to computing eigenvalues of the
           Stokes operator
    • Abstract: Abstract The eigenvalues and eigenfunctions of the Stokes operator have been the subject of intense analytical investigation and have applications in the study and simulation of the Navier–Stokes equations. As the Stokes operator is second order and has the divergence-free constraint, computing these eigenvalues and the corresponding eigenfunctions is a challenging task, particularly in complex geometries and at high frequencies. The boundary integral equation (BIE) framework provides robust and scalable eigenvalue computations due to (a) the reduction in the dimension of the problem to be discretized and (b) the absence of high-frequency “pollution” when using Green’s function to represent propagating waves. In this paper, we detail the theoretical justification for a BIE approach to the Stokes eigenvalue problem on simply- and multiply-connected planar domains, which entails a treatment of the uniqueness theory for oscillatory Stokes equations on exterior domains. Then, using well-established techniques for discretizing BIEs, we present numerical results which confirm the analytical claims of the paper and demonstrate the efficiency of the overall approach.
      PubDate: 2020-03-03
       
  • The nonconforming virtual element method for fourth-order singular
           perturbation problem
    • Abstract: Abstract We present the nonconforming virtual element method for the fourth-order singular perturbation problem. The virtual element proposed in this paper is a variant of the C0-continuous nonconforming virtual element presented in our previous work and allows to compute two different projection operators that are used for the construction of the discrete scheme. We show the optimal convergence in the energy norm for the nonconforming virtual element method. Further, the lowest order nonconforming method is proved to be uniformly convergent with respect to the perturbation parameter. Finally, we verify the convergence for the nonconforming virtual element method by some numerical tests.
      PubDate: 2020-02-27
       
  • On the accurate evaluation of unsteady Stokes layer potentials in moving
           two-dimensional geometries
    • Abstract: Abstract Two fundamental difficulties are encountered in the numerical evaluation of time-dependent layer potentials. One is the quadratic cost of history dependence, which has been successfully addressed by splitting the potentials into two parts—a local part that contains the most recent contributions and a history part that contains the contributions from all earlier times. The history part is smooth, easily discretized using high-order quadratures, and straightforward to compute using a variety of fast algorithms. The local part, however, involves complicated singularities in the underlying Green’s function. Existing methods, based on exchanging the order of integration in space and time, are able to achieve high-order accuracy, but are limited to the case of stationary boundaries. Here, we present a new quadrature method that leaves the order of integration unchanged, making use of a change of variables that converts the singular integrals with respect to time into smooth ones. We have also derived asymptotic formulas for the local part that lead to fast and accurate hybrid schemes, extending earlier work for scalar heat potentials and applicable to moving boundaries. The performance of the overall scheme is demonstrated via numerical examples.
      PubDate: 2020-02-27
       
  • Stochastic Bernstein polynomials: uniform convergence in probability with
           rates
    • Abstract: Abstract We introduce stochastic variants of the classical Bernstein polynomials associated with a continuous function f, built up from a general triangular array of random variables. We discuss the uniform convergence in probability of the approximation process that they represent, providing at the same time rates of convergence. In the particular case in which the triangular array of random variables consists of the uniform order statistics, we give a positive answer to a conjectured raised in Wu and Zhou (Adv. Comput. Math. 46, 8, 2020) about an exponential rate of convergence in probability.
      PubDate: 2020-02-27
       
 
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