Sinc-collocation Methods Research Articles

Electronic spectrum of linear Schrodinger equations by Sinc-Galerkin and Sinc-Collocation methods

Electronic spectrum of linear Schrodinger equations by Sinc-Galerkin and Sinc-Collocation methods

Solution of mediated bioelectrocatalysis process related to the Michaelis‐Menten equation by sinc method

AbstractIn this study, sinc‐Galerkin and Sinc collocation methods coupled with double exponential transformation have been developed to obtain a numerical solution of nonlinear two‐point boundary value problem arising in steady state nonlinear reaction diffusion equation containing a nonlinear term related to Michaelis‐Menten of the enzymatic reaction. Application of these methods reduce the solution of the Michaelis‐Menten equation to the solution of nonlinear system of algebraic equations. The upper bound of the error was calculated. Two problems of this model, chosen from the literature, were considered and for several parameters, numerical solution was shown. Obtained numerical results and error of the methods show that these methods are very fast with high efficiency in convergence.

Theoretical analysis of Sinc-collocation methods and Sinc-Nyström methods for systems of initial value problems

A Sinc-collocation method has been proposed by Stenger, and he also gave theoretical analysis of the method in the case of a `scalar' equation. This paper extends the theoretical results to the case of a `system' of equations. Furthermore, this paper proposes more efficient method by replacing the variable transformation employed in Stenger's method. The efficiency is confirmed by both of theoretical analysis and numerical experiments. In addition to the existing and newly-proposed Sinc-collocation methods, this paper also gives similar theoretical results for Sinc-Nystr\"{o}m methods proposed by Nurmuhammad et al. From a viewpoint of the computational cost, it turns out that the newly-proposed Sinc-collocation method is the most efficient among those methods.

第二種積分方程式に対するSinc選点法の改良とその理論解析(平成25年度日本応用数理学会論文賞(理論部門)受賞論文紹介)

第二種積分方程式に対するSinc選点法の改良とその理論解析(平成25年度日本応用数理学会論文賞(理論部門)受賞論文紹介)

Numerical Solution of Nonlinear Weakly Singular Fredholm-Volterra Integral Equations of the Second Kind by Using Sinc-Collocation Methods

Numerical Solution of Nonlinear Weakly Singular Fredholm-Volterra Integral Equations of the Second Kind by Using Sinc-Collocation Methods

Collocation method using quintic B-spline and sinc functions for solving a model of squeezing flow between two infinite plates

An axisymmetric viscous flow, generated by two large parallel plates slowly approaching each other is investigated. The steady nonlinear governing equations are converted into a fourth-order nonlinear differential equation using integrability condition. The resulting nonlinear boundary value problem is solved using quintic B-spline collocation and sinc-collocation methods. The approach consists of reducing the problem to a set of algebraic equations. Numerical examples are included to demonstrate the validity and applicability of the techniques and a comparison is made with existing results in the literature.

Solving differential equations using Sinc-collocation methods with derivative interpolations

Solving differential equations using Sinc-collocation methods with derivative interpolations

Convergence analysis of Sinc-collocation methods for nonlinear Fredholm integral equations with a weakly singular kernel

In this paper, the efficient methods are proposed for solving nonlinear Fredholm integral equations with a weakly singular kernel. By using Sinc approximation with the single exponential (SE) and double exponential (DE) transformations, the methods are developed. Sinc approximation has considerable advantages. Approximation by Sinc functions handles singularities in the problem and such approximations yield rapidly convergent schemes for solving the problem. Furthermore, convergence of proposed methods is discussed by preparing the theorems which show exponential convergence and guarantee the applicability of those. Finally, some numerical examples are presented to illustrate efficiency and accuracy of the numerical schemes.

Sinc Collocation Method for Finding Numerical Solution of Integrodifferential Model Arisen in Continuous Mixed Strategy

One of the new techniques is used to solve numerical problems involving integral equations and ordinary differential equations known as Sinc collocation methods. This method has been shown to be an efficient numerical tool for finding solution. The construction mixed strategies evolutionary game can be transformed to an integrodifferential problem. Properties of the sinc procedure are utilized to reduce the computation of this integrodifferential to some algebraic equations. The method is applied to a few test examples to illustrate the accuracy and implementation of the method.

A Sinc-Galerkin technique for the numerical solution of a class of singular boundary value problems

Singular boundary value problems have received considerable interest in the mathematical applications in different areas of science and engineering. Due to the presence of a singularity, these problems raise difficulties in obtaining their analytic or numerical solutions, and various schemes have been proposed to overcome these difficulties. However, among existing techniques, the Sinc-Galerkin and Sinc-collocation methods are well-suited for handling the singularity and have high performance on boundary value problems with unbounded domains. In this work, the Sinc-Galerkin scheme is implemented to find a numerical solution of singular two-point boundary value problems arising in various physical models. Some properties of the Sinc-Galerkin method required for our subsequent development are given and are utilized to reduce the computation of solution of singular boundary value problem (BVP) to some nonlinear systems of equations. The accuracy and reliability of the proposed method are demonstrated by five test problems arising in physiology and engineering. The results are found to be in good agreement with the numerical/exact/available solutions.

Sinc-Galerkin and Sinc-Collocation methods in the solution of nonlinear two-point boundary value problems

A comparative study of the Sinc-Galerkin and Sinc-Collocation methods for solving singular and nonsingular nonlinear second-order two-point boundary value problems (BVPs) with nonhomogeneous boundary conditions is given. We developed the Sinc-Galerkin and Sinc-Collocation methods to approximate the nonlinear two-point BVPs. These method are tested on the test examples and compared with several existing methods. The demonstrated results show that both of the presented methods more or less have the same accuracy, but in comparison with the other existing methods are considerable accurate.

Modified Sinc-collocation methods for integral equations of the second kind and their theoretical analysis(Theory)

Modified Sinc-collocation methods for integral equations of the second kind and their theoretical analysis(Theory)

Sinc-collocation methods for weakly singular Fredholm integral equations of the second kind

In this paper we propose new numerical methods for linear Fredholm integral equations of the second kind with weakly singular kernels. The methods are developed by means of the Sinc approximation with smoothing transformations, which is an effective technique against the singularities of the equations. Numerical examples show that the methods achieve exponential convergence, and in this sense the methods improve conventional results where only polynomial convergence have been reported so far.

Sinc-Collocation Methods for the Solution of Hallen's Integral Equation

The Sinc-collocation method is presented for solving Hallen's integral equations. Properties of Sinc functions are first presented, these properties are then utilized to reduce the computation of Hallen's integral equations to some linear algebraic equations. The method is computationally attractive, and applications are demonstrated through an illustrative example.

Sinc methods for domain decomposition

Sinc basis functions form a desirable basis for solving singular problems via domain decomposition. This is because both the Sinc-Galerkin and sinc-collocation methods converge exponentially, even in the presence of boundary singularities. This suggests the future possibility of combining sinc methods used in the vicinity of singularities with other methods, such as finite difference methods, used in the remainder of the original domain. For these reasons, a thorough investigation of the implementation of sinc methods in the context of domain decomposition is the necessary first step. This work deals with sinc methods for second-order ordinary differential equations with homogeneous Dirichlet boundary conditions. Both sinc-collocation and Sinc-Galerkin methods are presented. The two traditional methods of domain decomposition, overlapping and patching, are described. Thus all the groundwork is laid to readily determine which method is most suited to any given problem. Numerical results are presented for both decomposition methods that exhibit the nearly identical errors achieved whether one uses the sinc-collocation method or the Sinc-Galerkin method.