Abstract
The application of the sinc-Galerkin method to an approximate solution of second-order singular Dirichlet-type boundary value problems were discussed in this study. The method is based on approximating functions and their derivatives by using the Whittaker cardinal function. The differential equation is reduced to a system of algebraic equations via new accurate explicit approximations of the inner products without any numerical integration which is needed to solve matrix system. This study shows that the sinc-Galerkin method is a very effective and powerful tool in solving such problems numerically. At the end of the paper, the method was tested on several examples with second-order Dirichlet-type boundary value problems.
Highlights
Sinc methods were introduced by Frank Stenger in [ ] and expanded upon by him in [ ]
The fully sinc-Galerkin method was developed for a family of complex-valued partial differential equations with time-dependent boundary conditions [ ]
Some novel procedures of using sinc methods to compute solutions to three types of medical problems were illustrated in [ ], and sincbased algorithm was used to solve a nonlinear set of partial differential equations in [ ]
Summary
Sinc methods were introduced by Frank Stenger in [ ] and expanded upon by him in [ ]. The paper [ ] illustrates the application of a sinc-Galerkin method to an approximate solution of linear and nonlinear second-order ordinary differential equations, and to an approximate solution of some linear elliptic and parabolic partial differential equations in the plane. The fully sinc-Galerkin method was developed for a family of complex-valued partial differential equations with time-dependent boundary conditions [ ]. Some novel procedures of using sinc methods to compute solutions to three types of medical problems were illustrated in [ ], and sincbased algorithm was used to solve a nonlinear set of partial differential equations in [ ]. The work which was presented in [ ] deals with the sinc-Galerkin method for solving nonlinear fourth-order differential equations with homogeneous and nonhomogeneous boundary conditions. In [ ], sinc methods were used to solve second-order ordinary differential equations with homogeneous Dirichlet-type boundary conditions
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