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 Computational and Applied MathematicsJournal Prestige (SJR): 0.272 Citation Impact (citeScore): 1Number of Followers: 3      Hybrid journal (It can contain Open Access articles) ISSN (Print) 0101-8205 - ISSN (Online) 1807-0302 Published by Springer-Verlag  [2469 journals]
• Bifurcation analysis of an intraguild predator-prey model

Abstract: Abstract This paper deals with a predator-prey model and a modified version consisting of a resource-consumer with two consumer species. We analyze the stability of equilibria and for the interior equilibrium, we show that the system undergoes some generic bifurcations such as fold, Hopf and Hopf-zero bifurcations. We characterize these bifurcations by the center manifold theorem and the normal form theory. We further compute the critical normal form coefficients of the reduced system to the center manifold and conclude the non-degeneracy conditions for the computed bifurcations. By using the numerical continuation method, we compute several bifurcation curves emanating from the detected bifurcation points to examine the obtained analytical results as well as to reveal further complex dynamical behaviors of the system which can not be achieved analytically. Especially for both the original and modified models on the Hopf bifurcation curve, we detect some codimension two bifurcations namely Hopf-zero and generalized Hopf.
PubDate: 2022-05-22

• A meshfree technique for the numerical solutions of nonlinear
Fornberg–Whitham and Degasperis–Procesi equations with their modified
forms

Abstract: Abstract An efficient and robust hybrid scheme based on radial basis functions (RBFs) and finite difference is implemented to solve nonlinear partial differential equations (PDEs). In the proposed method, first-order finite difference and the $$\theta$$ -weighted scheme are coupled for temporal discretization, while RBFs are used for spatial discretization. The key feature of the scheme is to use quasilinearization with a collocation approach to reduce nonlinear PDEs to linear algebraic system of equations which are easy to solve. Stability analysis is carried out to examine the spectral radius of the amplification matrix versus the shape parameter. Furthermore, the scheme is applied to solve some nonlinear PDEs including Fornberg–Whitham, Degasperis–Procesi equations, and their modified forms. Efficiency of the proposed technique is demonstrated via different error norms and conservative quantities. Moreover, the computed results are compared with the existing results in the literature. Simulations reveal better accuracy for the considered problems.
PubDate: 2022-05-19

• Numerical and theoretical approximation results for Schurer–Stancu
operators with shape parameter $$\lambda$$ λ

Abstract: Abstract In this paper, we focus on pointwise and weighted approximation properties of newly defined Stancu variant of $$\lambda$$ -Schurer operators. We establish a direct local approximation theorem and obtain a global approximation formula. These newly defined operators reduce to classical Schurer, Bernstein, Stancu, $$\lambda$$ -Bernstein, $$\lambda$$ -Stancu, $$\lambda$$ -Schurer operators for the special cases of parameters. Certain illustrative and numerical examples are given to verify the convergence behavior and accuracy of the proposed operators. The numerical evaluations that obtained in this study may facilitate understanding and interpreting main results of this paper for the reader.
PubDate: 2022-05-17

• Applications of generalized fixed points theorems to the existence of
uncertainly hyperbolic partial differential equations with finite delay

Abstract: Abstract We study the existence and uniqueness of solutions for a boundary value problem associated with a class of fuzzy hyperbolic partial differential equations with finite delay. We establish a more general definition of integral solutions for the boundary value problem and, using some results of fixed point of weakly contractive mappings on partially ordered metric spaces, we prove that the existence of just a lower or an upper solution is enough to prove the existence and uniqueness of fuzzy solutions in the setting of a generalized Hukuhara derivative. Our existence results generalize, extend, and improve different results existing in the literature about this problem.
PubDate: 2022-05-17

• Improving the space-filling behavior of multiple triple designs

Abstract: Abstract A space-filling (SF) design gives a good representation of experimental region with even fewer points by selecting its points everywhere in the region with as few gaps as possible. Elsawah (J Comput Appl Math 384:113164, 2021) presented the multiple tripling (MT) technique for constructing a new class of three-level designs, called multiple triple designs (MTDs). The MT technique showed its superiority over the widely used techniques by constructing new large optimal MTDs in an efficient manner using small initial designs (InDs). This paper gives a closer look at the SF behavior of MTDs after all of its factor projections and level permutations (FPs-LPs) that alter their statistical inference abilities. The selection of optimal designs by FPs-LPs of such large MTDs needs millions of trials to test all the possible cases. This paper tries to solve this hard computational problem by building theoretical bridges between the SF behavior of the MTD after all of its FPs-LPs and the behavior of the corresponding InD, which is investigated based on the similarity among its runs, confounding among its factors, and uniformity of its points. This study provides benchmarks to guide the experimenters before using FPs-LPs for improving the SF behavior of MTDs in the full dimension and any low dimension. Moreover, the construction of non-isomorphic MTDs is discussed and a lower bound of the number of non-isomorphic MTDs is given. Finally, numerical studies to support the interesting theoretical findings are provided.
PubDate: 2022-05-17

• On the second order of accuracy stable difference scheme for integral type
non-local elliptic source identification problem

Abstract: Abstract In this study, a source identification problem for elliptic differential equation with integral type non-local condition is discussed. The second order of accuracy difference scheme for elliptic non-local source identification problem is studied. Using spectral resolution of a self-adjoint operator, stability and coercive stability estimates for solution of difference scheme are established. Subsequently, difference scheme for an approximate solution of multi-dimensional boundary-value problem with integral type non-local and first kind boundary conditions is investigated for stability. Numerical results for 2D and 3D examples are illustrated.
PubDate: 2022-05-16

• An effective algorithm for mean curvature-based image deblurring problem

Abstract: Abstract The mean curvature-based image deblurring model is widely used in image restoration to preserve edges and remove staircase effect in the resulting images. However, the Euler–Lagrange equations of the mean curvature model lead to the challenging problem of solving a nonlinear fourth order integro-differential equation. Furthermore the discretization of the Euler–Lagrange equations produces a nonlinear ill-conditioned system which affects the convergence of the numerical algorithms such as Krylov subspace methods (GMRES, etc.) In this paper, we have treated the high order nonlinearity by converting the nonlinear fourth order integro-differential equation into a system of first order equations. To speed up convergence by GMRES method, we have introduced a new circulant preconditioned matrix. Fast convergence is assured by the proved analytical property of our proposed new preconditioner. The first order error estimates are also established for the finite difference discretization. The effectiveness of our algorithm can be observed through fast convergence rates in numerical examples.
PubDate: 2022-05-16

• Abundant accurate solitonic water and ionic liquid wave structures of the
nanoparticle hybrid system

Abstract: Abstract This study gives more attention to soliton wave solutions of the nanoparticle hybrid system through two recent (generalized rational (GRat) and Kudryashov (GKud)) schemes. Because of the hybrid model’s nanoscale size, the nanoparticles in these new solitonic liquid wave structures exhibit unique electrical and optical characteristics crucial to several applications. The constructed results are numerically simulated in polar, contour, two, and three-dimensional graphs to demonstrate the dynamic behavior of an inviscid, incompressible, and non-rotating flow of fluid of constant depth h. Moreover, the obtained solutions’ accuracy is also checked by implementing two precise numerical (quintic-B-spline (QBS) and septic-B-spline (SBS)) schemes. The matching between computational and approximate solutions is explained through some distinct graphs in two-dimensional and distribution graphs. The novelty of our results is also elucidated by comparing our results with those constructed previously.
PubDate: 2022-05-16

• A new subspace minimization conjugate gradient method based on conic model
for large-scale unconstrained optimization

Abstract: Abstract Conjugate gradient method is one of the most efficient methods for large-scale unconstrained optimization and has attracted focused attention of researchers. With the emergence of more and more large-scale problems, subspace technique becomes particularly important. Recently, many scholars have studied subspace minimization conjugate gradient methods, where the iteration direction is generally obtained by minimizing a quadratic approximate model in a specific subspace. Considering that the conic model contains more information than the quadratic model, and may perform better when the objective function is not close to quadratic, in this paper, a improved conjugate gradient method is presented. Specially, in each iteration, a quadratic or conic model is dynamically selected. The search direction is obtained by minimizing the selected model in a three-dimensional subspace spanned by the current gradient and latest two search directions. It is proved that the search direction satisfies the sufficient descent condition under given conditions. With the modified nonmonotone Wolfe line search, we establish the global convergence and the R-linear convergence of the proposed method under mild assumptions. Numerical experiments indicate that the proposed method is efficient.
PubDate: 2022-05-16

• Hemivariational inequalities on graphs

Abstract: Abstract In this paper, a new class of hemivariational inequalities is introduced. It concerns Laplace operator on locally finite graphs together with multivalued nonmonotone nonlinearities expressed in terms of Clarke’s subdifferential. First of all, we state and prove some results on the subdifferentiability of nonconvex functionals defined on graphs. Thereafter, an elliptic hemivariational inequality on locally finite graphs is considered and the existence and uniqueness of its weak solutions are proved by means of the well-known surjectivity result for pseudomonotone mappings. In the end of this paper, we tackle the problem of hemivariational inequalities of parabolic type on locally finite graphs and we prove the existence of its weak solutions.
PubDate: 2022-05-13

• Ample felicitous wave structures for fractional foam drainage equation
modeling for fluid-flow mechanism

Abstract: Abstract In this study, traveling wave solutions have been explored with the newly developed improved tanh method and modified $$\left( {1/G^{\prime}} \right)$$ -expansion method for the Fractional foam drainage equation, which is famous for modeling physical phenomena such as heat conduction and acoustic waves. Abundant solutions are successfully achieved which have not been appeared ever in the literature. The found solutions are represented graphically to bring out the appearances of different types solitons. In addition, three important points are highlighted in the result and discussion section. First, the comparison of the applied methods, second, the association of the obtained solutions with the literature, and finally the effect of the change in the parameters with physical properties on the wave behavior are discussed.
PubDate: 2022-05-12

• A new hybrid regularization scheme for removing salt and pepper noise

Abstract: Abstract We propose a new model for removing the Salt and Pepper Noise (SPN) by combining the high-order total variation overlapping group sparsity with the nuclear norm regularization. Since the proposed model is convex, non-smooth, and separable, the alternating direction method of multipliers (ADMM) can be employed to solve it and the convergence can be kept. Numerical comparisons with some related state-of-the-art models show that the proposed model can significantly improve the restored quality in terms of the signal to noise ratio (SNR) and the structural similarity index measure (SSIM).
PubDate: 2022-05-12

• $$\mathbb {Z}_2\mathbb {Z}_2[u^4]$$ Z 2 Z 2 [ u 4 ] -cyclic codes and
their duals

Abstract: Abstract In this paper, we study the algebraic structure of a new family of linear codes over the mixed alphabet $${\mathbb {Z}}_2\mathrm {R}$$ , where $$\mathrm {R}={\mathbb {Z}}_2+u{\mathbb {Z}}_2+u^2{\mathbb {Z}}_2+u^3{\mathbb {Z}}_2, \ u^4=0$$ . We present generator and parity-check matrices of $${\mathbb {Z}}_2\mathrm {R}$$ -linear codes in standard form. We define a $${\mathbb {Z}}_2\mathrm {R}$$ -cyclic code of length (r, s) as a $$\mathrm {R}[x]$$ -submodule of $$\frac{{\mathbb {Z}}_2[x]}{\langle x^r-1 \rangle } \times \frac{\mathrm {R}[x]}{\langle x^s-1 \rangle }$$ and determine its generator polynomial. Also, we determine the size of a $${\mathbb {Z}}_2\mathrm {R}$$ -cyclic code by giving a minimal spanning set. Furthermore, we present the generator polynomial of dual code of a $${\mathbb {Z}}_2\mathrm {R}$$ -cyclic code of length (r, s) for odd s, while r is set arbitrary. Finally, optimal binary codes are constructed from Gray images of $${\mathbb {Z}}_2\mathrm {R}$$ -cyclic codes.
PubDate: 2022-05-11

• A novel claim size distribution based on a Birnbaum–Saunders and gamma
mixture capturing extreme values in insurance: estimation, regression, and
applications

Abstract: Abstract Data including significant losses are a pervasive issue in general insurance. The computation of premiums and reinsurance premiums, using deductibles, in situations of heavy right tail for the empirical distribution, is crucial. In this paper, we propose a mixture model obtained by compounding the Birnbaum–Saunders and gamma distributions to describe actuarial data related to financial losses. Closed-form credibility and limited expected value premiums are obtained. Moment estimators are utilized as starting values in the non-linear search procedure to derive the maximum-likelihood estimators and the asymptotic variance–covariance matrix for these estimators is determined. In comparison to other competing models commonly employed in the actuarial literature, the new mixture distribution provides a satisfactory fit to empirical data across the entire range of their distribution. The right tail of the empirical distribution is essential in the modeling and computation of reinsurance premiums. In addition, in this paper, to make advantage of all available data, we create a regression structure based on the compound distribution. Then, the response variable is explained as a function of a set of covariates using this structure.
PubDate: 2022-05-11

• Auction design for the allocation of carbon emission allowances to supply
chains via multi-agent-based model and Q-learning

Abstract: Abstract To increase competition, control price, and decrease inefficiency in the carbon allowance auction market, limitations on bidding price and volume can be set. With limitations, participants have the same cap bidding price and volume. While without the limitations, participants have different values per unit of carbon allowance; therefore, some participants may be strong and the other week. Due to the impact of these limitations on the auction, this paper tries to compare the uniform and discriminatory pricing in a carbon allowance auction with and without the limitations utilizing a multi-agent-based model consisting of the government and supply chains. The government determines the supply chains' initial allowances. The supply chains compete in the carbon auction market and determine their bidding strategies based on the Q-learning algorithm. Then they optimize their tactical and operational decisions. They can also trade their carbon allowances in a carbon trading market in which price is free determined according to carbon supply and demand. Results show that without the limitations, the carbon price in the uniform pricing is less than or equal to the discriminatory pricing method. At the same time, there are no differences between them in the case with limitations. Overall, the auction reduces the profit of the supply chains. This negative effect is less in uniform than discriminatory pricing in the case without the limitations. Nevertheless, the strong supply chains make huge profits from the auction when mitigation rate is high.
PubDate: 2022-05-10

• A mixed method approach to the solitary wave, undular bore and
boundary-forced solutions of the Regularized Long Wave equation

Abstract: Abstract The aim of the present work is to obtain numerical solutions of the solitary wave, undular bore and boundary-forced problems for Regularized Long Wave (RLW) equation. For this purpose, low-order modified cubic B-spline is chosen as base functions. Crank–Nicolson formulae combined with efficient space discretization method have been applied. With the aid of Rubin and Graves type linearization technique, nonlinear terms are linearized and a solvable linear equation system has been obtained. Three significant test problems in the literature are solved successfully. The present algorithm has obtained high accurate numerical solutions of the RLW equation. Numerical results are compared with those of some earlier ones and given. The rates of the convergence are also investigated.
PubDate: 2022-05-10

• Relationships between two pairs of covering approximation operators and
belief structures

Abstract: Abstract As two mathematical tools for dealing with uncertainty, the covering rough set theory and the evidence theory have close relationships with each other. Different covering rough set models are characterized by evidence theory. The purpose of this paper is to interpret belief functions with two pairs of covering approximation operators. The two pairs of covering approximation operators are equivalent to a pair of relation approximation operators. Then, based on a necessary and sufficient condition for a belief structure to be the belief structure induced by the pair of relation approximation operators, necessary and sufficient conditions for a belief structure to be the belief structure induced by the covering approximation operators are presented. Moreover, two kinds of covering reductions in covering information systems defined from the two pairs of covering approximation operators are characterized by the belief and plausibility functions.
PubDate: 2022-05-07

• A constrained system of matrix equations

Abstract: Abstract Sylvester-type matrix equations have wide applications in system science, control theory, and so on. In this paper, we consider a constrained system of Sylvester-type matrix equations over the quaternions. We first derive the necessary and sufficient conditions for the system to have a solution and propose a formula of its general solution when it is solvable. As an application, we then investigate the $$\eta$$ -Hermitian solution of a system. Moreover, we also give a numerical example to illustrate the main findings of this paper.
PubDate: 2022-05-06

• A shape design problem for the Navier–Stokes flow with a convective
boundary condition

Abstract: Abstract In this study, a shape optimization problem for the two-dimensional stationary Navier–Stokes equations with an artificial boundary condition is considered. The fluid is assumed to be flowing through a rectangular channel, and the artificial boundary condition is formulated so as to take into account the possibility of ill-posedness caused by the usual do-nothing boundary condition. The goal of the optimization problem is to maximize the vorticity of the said fluid by determining the shape of an obstacle inside the channel. Meanwhile, the shape variation is limited by a perimeter functional and a volume constraint. The perimeter functional was considered to act as a Tikhonov regularizer and the volume constraint is added to exempt us from possible topological changes. The shape derivative of the objective functional was formulated using the rearrangement method, and this derivative was later on used for gradient descent methods. Additionally, an augmented Lagrangian method and a class of solenoidal deformation fields were considered to take into account the goal of volume preservation. Lastly, numerical examples based on gradient descent and the volume preservation methods are presented.
PubDate: 2022-05-06

• A novel low-rank matrix approximation algorithm for face denoising and
background/foreground separation

Abstract: Abstract Low-rank matrix recovery from an observation data matrix has received considerable attention in recent years, which has a wide range of applications in pattern recognition and computer vision, such as face denoising, background/foreground separation, gait recognition, image alignment, etc. However, existing algorithms suffer from the interference of small noise, for example, low-level Gaussian noise, which makes their performance not satisfactory. To address this issue, we are based on the unconstrained nonconvex relaxed minimization model for low-rank and sparse matrices recovery using low-rank matrix decomposition, and propose a novel efficient and effective solving algorithm in terms of direction matrices and step sizes alternating iteration in this paper. The three direction matrices are deduced using Newton method, Taylor expansion and so forth, and the appropriate step size of the direction sparse matrix is searched by the nonmonotonous step size linear search technique efficiently. In theory, we provide the convergence theorem of the proposed algorithm. Experimentally, its efficiency and effectiveness are illustrated under appropriate conditions.
PubDate: 2022-05-05

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