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MATHEMATICS (642 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 4)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 2)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 6)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 16)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 4)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Full-text available via subscription   (Followers: 21)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 10)
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: 5)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 5)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 3)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 2)
Advances in Catalysis     Full-text available via subscription   (Followers: 5)
Advances in Complex Systems     Hybrid Journal   (Followers: 7)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 15)
Advances in Decision Sciences     Open Access   (Followers: 4)
Advances in Difference Equations     Open Access   (Followers: 1)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 9)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 1)
Advances in Materials Sciences     Open Access   (Followers: 16)
Advances in Mathematical Physics     Open Access   (Followers: 6)
Advances in Mathematics     Full-text available via subscription   (Followers: 10)
Advances in Numerical Analysis     Open Access   (Followers: 3)
Advances in Operations Research     Open Access   (Followers: 11)
Advances in Porous Media     Full-text available via subscription   (Followers: 4)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 5)
Advances in Pure Mathematics     Open Access   (Followers: 4)
Advances in Science and Research (ASR)     Open Access   (Followers: 6)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 5)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 4)
Afrika Matematika     Hybrid Journal   (Followers: 1)
Air, Soil & Water Research     Open Access   (Followers: 7)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Algebra and Logic     Hybrid Journal   (Followers: 2)
Algebra Colloquium     Hybrid Journal   (Followers: 4)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Full-text available via subscription   (Followers: 5)
Algorithms     Open Access   (Followers: 9)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Biostatistics     Open Access   (Followers: 9)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 3)
American Journal of Mathematical Analysis     Open Access  
American Journal of Mathematics     Full-text available via subscription   (Followers: 7)
American Journal of Operations Research     Open Access   (Followers: 5)
American Mathematical Monthly     Full-text available via subscription   (Followers: 6)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 7)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access   (Followers: 1)
Analysis     Hybrid Journal   (Followers: 2)
Analysis and Applications     Hybrid Journal   (Followers: 1)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 4)
Analysis Mathematica     Full-text available via subscription  
Annales Mathematicae Silesianae     Open Access  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annales UMCS, 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: 3)
Annals of Data Science     Hybrid Journal   (Followers: 8)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 6)
Annals of Mathematics     Full-text available via subscription  
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 6)
Annals of Pure and Applied Logic     Open Access   (Followers: 2)
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  
Annuaire du Collège de France     Open Access   (Followers: 5)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applications of Mathematics     Hybrid Journal   (Followers: 1)
Applied Categorical Structures     Hybrid Journal   (Followers: 2)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 12)
Applied Mathematics     Open Access   (Followers: 3)
Applied Mathematics     Open Access   (Followers: 4)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 4)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 1)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 4)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 2)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 1)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 4)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 4)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites : The Journal of Space Research Centre of Polish Academy of Sciences     Open Access   (Followers: 17)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian Journal of Current Engineering & Maths     Open Access  
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 2)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 7)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 2)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access  
Baltic International Yearbook of Cognition, Logic and Communication     Open Access  
Basin Research     Hybrid Journal   (Followers: 3)
BIBECHANA     Open Access  
BIT Numerical Mathematics     Hybrid Journal  
BoEM - Boletim online de Educação Matemática     Open Access  
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: 1)
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: 6)
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: 1)
Bulletin of Mathematical Sciences     Open Access   (Followers: 2)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 3)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Calculus of Variations and Partial Differential Equations     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 18)
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CEAS Space Journal     Hybrid Journal  
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 3)
ChemSusChem     Hybrid Journal   (Followers: 7)
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  
Clean Air Journal     Full-text available via subscription   (Followers: 2)
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 4)
Collectanea Mathematica     Hybrid Journal  
College Mathematics Journal     Full-text available via subscription   (Followers: 1)
COMBINATORICA     Hybrid Journal  
Combustion Theory and Modelling     Hybrid Journal   (Followers: 13)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 1)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 3)
Complex Analysis and its Synergies     Open Access   (Followers: 2)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Complexus     Full-text available via subscription  
Composite Materials Series     Full-text available via subscription   (Followers: 9)
Comptes Rendus Mathematique     Full-text available via subscription   (Followers: 1)
Computational and Applied Mathematics     Hybrid Journal   (Followers: 2)
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: 8)
Computational Mechanics     Hybrid Journal   (Followers: 4)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 7)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 5)
Concrete Operators     Open Access   (Followers: 4)
Confluentes Mathematici     Hybrid Journal  
COSMOS     Hybrid Journal  
Cryptography and Communications     Hybrid Journal   (Followers: 12)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Czechoslovak Mathematical Journal     Hybrid Journal   (Followers: 1)
Demographic Research     Open Access   (Followers: 11)
Demonstratio Mathematica     Open Access  
Dependence Modeling     Open Access  
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 28)
Developments in Clay Science     Full-text available via subscription   (Followers: 1)
Developments in Mineral Processing     Full-text available via subscription   (Followers: 3)
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 2)
Discrete Mathematics     Hybrid Journal   (Followers: 7)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Doklady Mathematics     Hybrid Journal  
Duke Mathematical Journal     Full-text available via subscription   (Followers: 1)
Edited Series on Advances in Nonlinear Science and Complexity     Full-text available via subscription  
Electronic Journal of Graph Theory and Applications     Open Access   (Followers: 2)
Electronic Notes in Discrete Mathematics     Full-text available via subscription   (Followers: 2)
Elemente der Mathematik     Full-text available via subscription   (Followers: 3)
Energy for Sustainable Development     Hybrid Journal   (Followers: 9)
Enseñanza de las Ciencias : Revista de Investigación y Experiencias Didácticas     Open Access  
Ensino da Matemática em Debate     Open Access  
Entropy     Open Access   (Followers: 4)
ESAIM: Control Optimisation and Calculus of Variations     Full-text available via subscription   (Followers: 1)
European Journal of Combinatorics     Full-text available via subscription   (Followers: 4)
European Journal of Mathematics     Hybrid Journal   (Followers: 1)
European Scientific Journal     Open Access   (Followers: 2)
Experimental Mathematics     Hybrid Journal   (Followers: 3)
Expositiones Mathematicae     Hybrid Journal   (Followers: 2)
Facta Universitatis, Series : Mathematics and Informatics     Open Access  
Fasciculi Mathematici     Open Access  
Finite Fields and Their Applications     Full-text available via subscription   (Followers: 4)
Fixed Point Theory and Applications     Open Access   (Followers: 1)
Formalized Mathematics     Open Access   (Followers: 2)
Foundations and Trends® in Econometrics     Full-text available via subscription   (Followers: 4)
Foundations and Trends® in Networking     Full-text available via subscription   (Followers: 1)

        1 2 3 4 | Last

Journal Cover Differential Equations and Dynamical Systems
  [SJR: 0.475]   [H-I: 9]   [2 followers]  Follow
   Hybrid Journal Hybrid journal (It can contain Open Access articles)
   ISSN (Print) 0974-6870 - ISSN (Online) 0971-3514
   Published by Springer-Verlag Homepage  [2340 journals]
  • Looking for an Efficient and Safe Hyperthermia Therapy: Insights from a
           Partial Differential Equations Based Model
    • Authors: Maria C. Quintero; Juan M. Cordovez
      Pages: 137 - 150
      Abstract: Abstract In the present study, we formulate a boundary value problem that characterizes the light and heat transfer processes in a tissue during a hypothetical superficial hyperthermia therapy. The heating process is represented with a partial differential equations system (PDEs) consisting in the diffusion and bio-heat equations whereas the tissue damage process is modeled with the Arrhenius integral equation. The PDEs system is discretized using the method of lines to obtain an ordinary differential equations system that approximates the original PDEs. The resulting model is then numerically solved to obtain (1) the spatio-temporal distribution of both absorbed light and heat, (2) the volume of tissue effectively treated, and (3) the degree of thermal damage reached. Finally, we define an optimization problem to find a set of relevant parameter values that maximize the therapeutic effect while minimizing damage to healthy tissue. The results of this work could be useful for preclinical level research, in particular for the study of strategies that modify the physical properties of the target tissue for a safe and efficient heat therapy.
      PubDate: 2017-04-01
      DOI: 10.1007/s12591-015-0256-8
      Issue No: Vol. 25, No. 2 (2017)
  • An Analysis on Induced Numerical Oscillations by Lax-Friedrichs Scheme
    • Authors: Ritesh Kumar Dubey; Biswarup Biswas
      Pages: 151 - 168
      Abstract: Abstract Induced numerical oscillations in the computed solution by monotone schemes for hyperbolic conservation laws has been a focus of recent studies. In this work using a local maximum principle, the monotone stable Lax-Friedrichs (LxF) scheme is investigated to explore the cause of induced local oscillations in the computed solution. It expounds upon that LxF scheme is locally unstable and therefore exhibits induced such oscillations. The carried out analysis gives a deeper insight to characterize the type of data extrema and the solution region which cause local oscillations. Numerical results for benchmark problems are also given to support the theoretical claims.
      PubDate: 2017-04-01
      DOI: 10.1007/s12591-016-0311-0
      Issue No: Vol. 25, No. 2 (2017)
  • A Higher Order Numerical Implicit Method for Non-Linear Burgers’
    • Authors: Vijitha Mukundan; Ashish Awasthi
      Pages: 169 - 186
      Abstract: Abstract This paper proposes a higher order implicit numerical scheme to approximate the solution of the nonlinear partial differential equation (PDE). This equation is a simplified form of Navier–Stoke’s equation also known as Burgers’ equation. It is an important nonlinear PDE which arises frequently in mathematical modeling of turbulence in fluid dynamics. In order to handle nonlinearity a nonlinear transformation is used which converts the nonlinear PDE into a linear PDE. The linear PDE is semi-discretized in space by method of lines to yield a system of ordinary differential equations in time. The resulting system of differential equations is investigated and found to be a stiff system. A system of stiff differential equations is further discretized by a low-dispersion and low-dissipation implicit Runge–Kutta method and solved by using MATLAB 8.0. The proposed scheme is unconditionally stable. Moreover it is simple, easy to implement and requires less computational time. Finally, the adaptability of the scheme is demonstrated by means of numerical computations by taking three test problems. The present implicit scheme have been compared with existing schemes in literature which shows that the proposed scheme offers more accuracy with less computational time than the numerical schemes given in Jiwari (Comput Phys Comm 183:2413–2423, 2012), Kutluay et al. (J Comput Appl Math 103:251–261, 1998), Kutluay et al. (J Comput Appl Math 167:21–33, 2004).
      PubDate: 2017-04-01
      DOI: 10.1007/s12591-016-0318-6
      Issue No: Vol. 25, No. 2 (2017)
  • Numerical Solutions of Sixth Order Eigenvalue Problems Using Galerkin
           Weighted Residual Method
    • Authors: Md. Shafiqul Islam; Humaira Farzana; Samir Kumar Bhowmik
      Pages: 187 - 205
      Abstract: Abstract In this research article, we present Galerkin weighted residual (WRM) technique to find the numerically approximated eigenvalues of the sixth order linear Sturm–Liouville problems (SLP) and Bénard layer problems. In the current method, Bernstein polynomials are being employed as the basis functions and precise matrix formulation is derived for solving eigenvalue problems. Numerical examples with homogeneous boundary conditions are considered to verify the efficiency and implementation of the proposed method. The numerical results offered in this paper are also compared with those investigated by other numerical/analytical methods and the computed eigenvalues are in good agreement.
      PubDate: 2017-04-01
      DOI: 10.1007/s12591-016-0323-9
      Issue No: Vol. 25, No. 2 (2017)
  • A New Numerical Method Based on Non-Polynomial Spline in Tension
    • Authors: Ranjan Kumar Mohanty; Ravindra Kumar
      Pages: 207 - 222
      Abstract: Abstract In this paper, we derive a new three level implicit method of order two in time and three in space, based on spline in tension approximation for the numerical solution of one space dimensional quasi-linear second order hyperbolic partial differential equation on a variable mesh. We also study application of the proposed method to wave equation in polar coordinates. High order approximation at first time level is briefly discussed which is applicable to solve problems both on uniform and non-uniform mesh. Numerical results are given to illustrate the usefulness of the proposed method.
      PubDate: 2017-04-01
      DOI: 10.1007/s12591-015-0261-y
      Issue No: Vol. 25, No. 2 (2017)
  • A Third (Four) Order Accurate, Nine-Point Compact Scheme for
           Mildly-Nonlinear Elliptic Equations in Two Space Variables
    • Authors: Navnit Jha; Neelesh Kumar; Kapil K. Sharma
      Pages: 223 - 237
      Abstract: Abstract A new non-uniform grid third order of magnitude finite differencing formula for the numerical solution of mildly nonlinear elliptic equations in two space variables is presented. Families of compact schemes of order three and four are obtained on nine stencils. The resulting formula yields a tri-block-diagonal matrix and easily computed using Gauss–Seidel method or Newton method depending on linear or nonlinear behaviour of the elliptic equation. We describe error analysis and obtain necessary criterion for the convergence to the proposed compact scheme. It is easy to prove monotone and irreducibility of the Jacobian matrix by the help of graph theory. The numerical accuracy and order of convergence for the solution variables to Chaplygin equation, two dimensional steady state heat/mass transfer equation and Dupuit–Forchheimer groundwater model have been presented to justify the theoretical analysis.
      PubDate: 2017-04-01
      DOI: 10.1007/s12591-015-0263-9
      Issue No: Vol. 25, No. 2 (2017)
  • Numerical Study on Binary Nanofluid Convection in a Rotating Porous Layer
    • Authors: Jyoti Sharma; Urvashi Gupta; R. K. Wanchoo
      Pages: 239 - 249
      Abstract: Abstract The present paper investigates the convection in a binary nanofluid layer in porous medium under the influence of rotation using Darcy–Brinkman model. A set of partial differential equations based on conservation laws for binary nanofluid convection are solved using Normal mode technique and one term weighted residual method. The problem is analyzed for both stationary as well as oscillatory convection for free-free boundaries of the layer. The oscillatory motions come into existence for bottom heavy configuration of nanoparticles in the fluid layer. As far as thermal Rayleigh number is concerned, it does not show much variation with respect to different nanoparticles (alumina, copper, titanium oxide, silver) for bottom heavy configuration. Rotation parameter is found to stabilize the system significantly.
      PubDate: 2017-04-01
      DOI: 10.1007/s12591-015-0268-4
      Issue No: Vol. 25, No. 2 (2017)
  • Finite Volume Approximations for Size Structured Neuron Model
    • Authors: Santosh Kumar; Paramjeet Singh
      Pages: 251 - 265
      Abstract: Abstract The objective of this paper is to present and analyze numerical approximation for the size structured neuron model. We propose finite volume approximations based on upwind and Lax–Wendroff for the partial differential equation originating in size structured neuron model (Perthame and Ryzhik in J Differ Equ 210:155–177, 2005) which is a conservation laws with source term. The developed numerical methods are analyzed for consistency, stability, and convergence. We perform some numerical experiments to verify the predicted theory of the numerical approximations constructed in this paper.
      PubDate: 2017-04-01
      DOI: 10.1007/s12591-016-0276-z
      Issue No: Vol. 25, No. 2 (2017)
  • A Higher Order Accurate Numerical Method for Singularly Perturbed Two
           Point Boundary Value Problems
    • Authors: Aditya Kaushik; Vijayant Kumar; Anil K. Vashishth
      Pages: 267 - 285
      Abstract: Abstract In this paper, an extended mixed asymptotic-numerical method is presented for a one dimensional two point singularly perturbed boundary value problem. The original problem is solved separately on outer and inner region. The outer region problem called the reduced problem is solved using the q-stage Runge-Kutta method and the inner region problem is solved asymptotically. A uniform error estimate of \(\mathcal {O}(h^p),\) \((p\le q)\) is obtained. Several numerical examples are taken to illustrate the comparative study. The method is also extended to delay and advance problem.
      PubDate: 2017-04-01
      DOI: 10.1007/s12591-016-0279-9
      Issue No: Vol. 25, No. 2 (2017)
  • A Robust Numerical Approach for Singularly Perturbed Time Delayed
           Parabolic Partial Differential Equations
    • Authors: Manju Sharma
      Pages: 287 - 300
      Abstract: Abstract A numerical study for a class of singularly perturbed partial functional differential equation has been initiated. The solution of the problem, being contaminated by a small perturbation parameter, exhibits layer behavior. There exist narrow regions, in the neighborhood of outflow boundary, where the solution has steep gradient. The presence of parasitic parameters, perturbation parameter and time delay, is often the source for the increased order and stiffness of these systems. The stiffness, attributed to the simultaneous occurrence of slow and fast phenomena and on their dependence on the past history of the physical systems. A numerical method based on standard finite difference operator is presented. The first step involves a discretization of time variable using backward Euler method. This results into a set of stationary singularly perturbed semi-discrete problems which are further discretized in space using standard finite difference operators. A priori explicit bounds on the solution of problem are established. Extensive amount of analysis is carried out in order to establish the convergence and stability of the method proposed.
      PubDate: 2017-04-01
      DOI: 10.1007/s12591-016-0280-3
      Issue No: Vol. 25, No. 2 (2017)
  • Parameter-Robust Numerical Method for Time-Dependent Weakly Coupled Linear
           System of Singularly Perturbed Convection-Diffusion Equations
    • Authors: S. Chandra Sekhara Rao; Varsha Srivastava
      Pages: 301 - 325
      Abstract: Abstract We present a parameter-robust numerical method for a time-dependent weakly coupled linear system of singularly perturbed convection-diffusion equations. A small perturbation parameter multiplies the second order spatial derivative in all the equations. The proposed numerical method uses backward Euler method in time direction on an uniform mesh together with a suitable combination of HODIE scheme and the central difference scheme in spatial direction on a Shishkin mesh. It is proved that the numerical method is parameter-robust of first order in time and almost second order in space. Numerical results are given in support of theoretical findings.
      PubDate: 2017-04-01
      DOI: 10.1007/s12591-016-0282-1
      Issue No: Vol. 25, No. 2 (2017)
  • Numerical Treatment for the Class of Time Dependent Singularly Perturbed
           Parabolic Problems with General Shift Arguments
    • Authors: Komal Bansal; Pratima Rai; Kapil K. Sharma
      Pages: 327 - 346
      Abstract: Abstract In this paper we design two numerical schemes for solving a class of time dependent singularly perturbed parabolic convection–diffusion problems with general shift arguments in the reaction term. The discretization in both the directions is based on finite difference scheme. Special type of mesh and interpolation is used to tackle the terms containing shifts. The earlier numerical schemes for the considered problem are restricted to the case of small delay and advance arguments while in practical situations these shift arguments can be of arbitrary size (i.e., may be big or small enough in size). In this paper we propose two numerical schemes which work in both the situations i.e., when shifts are big or small enough in size. An extensive amount of analysis is presented to show the linear convergence in space and time of both the schemes. Some numerical results are given to confirm the predicted theory and to show the effect of shifts on the solution.
      PubDate: 2017-04-01
      DOI: 10.1007/s12591-015-0265-7
      Issue No: Vol. 25, No. 2 (2017)
  • An Efficient Modified Haar Wavelet Collocation Method for Numerical
           Solution of Two-Dimensional Elliptic PDEs
    • Authors: Imran Aziz; Siraj-ul-Islam
      Pages: 347 - 360
      Abstract: Abstract In this work, we present a new method for solving elliptic partial differential equations using Haar wavelet. This work improves the earlier work (Aziz et al. in Appl Math Model 37:676–694, 2013) in terms of efficiency and contains an extension to nonlinear elliptic partial differential equations as well. In this paper the earlier algorithm (Aziz et al. in Appl Math Model 37:676–694, 2013) has been modified by starting the approximation with a fourth order mixed derivative rather than approximation of the second order derivatives with respect to x and y separately which results in a more efficient algorithm than the earlier algorithm. The use of Kronecker tensor products makes the new algorithm robust and easier to implement in a programming language. A distinguishing feature of the new method is that it can be applied to a variety of boundary conditions with a little modification of the program. The method is tested on several benchmark linear as well as nonlinear models. The numerical results show convergence, simple applicability and efficiency of the method.
      PubDate: 2017-04-01
      DOI: 10.1007/s12591-015-0262-x
      Issue No: Vol. 25, No. 2 (2017)
  • Numerical Approximation of an Elastic Wave Model
    • Authors: Samir Kumar Bhowmik; Abdullah Aljouiee
      Pages: 361 - 371
      Abstract: Abstract Wave operators play an important role modeling various physical, engineering and biological problems. We consider an initial boundary value problem modeling an elastic wave propagation. We approximate the model using a Legendre spectral Galerkin method for the spatial approximation. We analyze the accuracy of such a spatial approximation. We perform some numerical experiments to demonstrate the scheme.
      PubDate: 2017-04-01
      DOI: 10.1007/s12591-015-0254-x
      Issue No: Vol. 25, No. 2 (2017)
  • On Inverse Full State Hybrid Function Projective Synchronization For
           Continuous-time Chaotic Dynamical Systems with Arbitrary Dimensions
    • Authors: Adel Ouannas; Ahmad Taher Azar; Toufik Ziar
      Abstract: Abstract Referring to continuous-time chaotic dynamical systems, this paper investigates the inverse full state hybrid function projective synchronization (IFSHFPS) of non-identical systems characterized by different dimensions. By taking a master system of dimension n and a slave system of dimension m, the method enables each master system state to be synchronized with a linear combination of slave system states, where the scaling factor of the linear combination can be any arbitrary differentiable function. The approach, based on the Lyapunov stability theory and stability of linear continuous-time systems, presents some useful features: (i) it enables non-identical chaotic systems with different dimension \(n<m\) or \(n>m\) to be synchronized; (ii) it can be applied to a wide class of chaotic (hyperchaotic) systems for any differentiable scaling function; (iii) it is rigorous, being based on two theorems, one for the case \(n<m\) and the other for the case \(n>m\) . Two different numerical examples are reported. The examples clearly highlight the capability of the conceived approach in effectively achieving synchronized dynamics for any differentiable scaling function.
      PubDate: 2017-04-27
      DOI: 10.1007/s12591-017-0362-x
  • Uniformly Convergent Second Order Numerical Method for a Class of
           Parameterized Singular Perturbation Problems
    • Authors: D. Shakti; J. Mohapatra
      Abstract: Abstract In this article, a class of nonlinear singularly perturbed boundary value problems depending on a parameter are considered. To solve this class of problems; first we apply the backward Euler finite difference scheme on Shishkin type meshes [standard Shishkin mesh (S-mesh), Bakhvalov–Shishkin mesh (B–S-mesh)]. The convergence analysis is carried out and the method is shown to be convergent with respect to the small parameter and is of almost first order accurate on S-mesh and first order accurate on B–S-mesh. Then, to improve the accuracy of the computed solution from almost first order to almost second order on S-mesh and from first order to second order on B–S-mesh, the post-processing method namely, the Richardson extrapolation technique is applied. The proof for the uniform convergence of the proposed method is carried out on both the meshes. Numerical experiments indicate the high accuracy of the proposed method.
      PubDate: 2017-04-24
      DOI: 10.1007/s12591-017-0361-y
  • The Well-Posedness of Fractional Systems with Affine-Periodic Boundary
    • Authors: Fei Xu; Yong Li; Yixian Gao; Xu Xu
      Abstract: Abstract This paper is devoted to study the existence and uniqueness of solutions for a class of nonlinear fractional dynamical systems with affine-periodic boundary conditions. We can show that there exists a solution for an \(\alpha \) -fractional system via the homotopy invariance of Brouwer degree, where \(0<\alpha \le 1\) . Furthermore, using Gronwall–Bellman inequality, we can prove the uniqueness of the solution if the nonlinearity satisfies the Lipschitz continuity. We apply the main theorem to the fractional kinetic equation and fractional oscillator with constant coefficients subject to affine-periodic boundary conditions. And in appendix, we give the proof of the nonexistence of affine-periodic solution to a given \((\alpha ,Q,T)\) -affine-periodic system in the sense of Riemann–Liouville fractional integral and Caputo derivative for \(0<\alpha <1\) .
      PubDate: 2017-04-08
      DOI: 10.1007/s12591-017-0360-z
  • Well-Posedness for a System of Integro-Differential Equations
    • Authors: Irene Benedetti; Luca Bisconti
      Abstract: Abstract We give sufficient conditions for the existence, the uniqueness and the continuous dependence on initial data of the solution to a system of integro-differential equations with superlinear growth on the nonlinear term. As possible applications of our methods we consider two epidemic models: a perturbed versions of the well-known integro-differential Kendall SIR model, and a SIRS-like model.
      PubDate: 2017-04-04
      DOI: 10.1007/s12591-017-0359-5
  • Existence and Asymptotic Behavior of Positive Solutions for a Coupled
           Fractional Differential System
    • Authors: Sonia Ben Makhlouf; Majda Chaieb; Zagharide Zine El Abidine
      Abstract: Abstract In this paper, we take up the existence and the asymptotic behavior of positive and continuous solutions to the following coupled fractional differential system $$\begin{aligned} \left\{ \begin{array}{ll} \displaystyle D^{\alpha } u=a(x)\displaystyle u^{p }\displaystyle v^{r}\quad \text { in }(0,1) , \\ \displaystyle D^{\beta } v=b(x)\displaystyle u^{s }\displaystyle v^{q}\quad \text { in }(0,1) , \\ u(0)= u(1)= D^{\alpha -3}u(0)= u^{\prime }(1)=0,\\ v(0)= v(1)= D^{\beta -3}v(0)= v^{\prime }(1)=0, \end{array} \right. \end{aligned}$$ where \( \alpha , \beta \in (3,4]\) , \(p, q\in (-1,1)\) , \(r, s\in \mathbb {R}\) such that \((1- p )(1- q )- rs > 0\) , D is the standard Riemann–Liouville differentiation and a, b are nonnegative and continuous functions in (0, 1) allowed to be singular at \(x=0\) and \(x=1\) and they are required to satisfy some appropriate conditions related to Karamata regular variation theory.
      PubDate: 2017-03-25
      DOI: 10.1007/s12591-017-0358-6
  • Editorial
    • Authors: Kapil K. Sharma; R. K. Mohanty
      PubDate: 2017-02-07
      DOI: 10.1007/s12591-017-0347-9
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