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.

[1]  Bernard Bialecki,et al.  Sinc-Collection Methods for Two-Point Boundary Value Problems , 1991 .

[2]  P. Kelevedjiev.  Existence of positive solutions to a singular second order boundary value problem , 2002 .

[3]  Jalil Rashidinia,et al.  Solution of a Volterra integral equation by the Sinc-collocation method , 2007 .

[4]  R. K. Mohanty,et al.  An O(h4) accurate cubic spline TAGE method for nonlinear singular two point boundary value problems , 2004, Appl. Math. Comput..

[5]  Mohamed El-Gamel,et al.  On the Galerkin and collocation methods for two-point boundary value problems using sinc bases , 2008, Comput. Math. Appl..

[6]  Kamel Al-Khaled,et al.  SOME CONVERGENCE RESULTS ON SINC INTERPOLATION , 2003 .

[7]  A. S. V. Ravi Kanth,et al.  Higher order finite difference method for a class of singular boundary value problems , 2004, Appl. Math. Comput..

[8]  Mohamed El-Gamel,et al.  Sinc-Galerkin method for solving linear sixth-order boundary-value problems , 2004, Math. Comput..

[9]  Xian Xu,et al.  A note on singular nonlinear boundary value problems , 2004 .

[10]  Kenneth L. Bowers,et al.  Sinc methods for quadrature and differential equations , 1987 .

[11]  Jalil Rashidinia,et al.  Approximate solution of systems of Volterra integral equations with error analysis , 2010, Int. J. Comput. Math..

[12]  F. Stenger.  Numerical Methods Based on Sinc and Analytic Functions , 1993 .

[13]  Yansheng Liu,et al.  Existence and uniqueness of positive solution for singular boundary value problem , 2005 .

[14]  Fazhan Geng,et al.  Solving singular nonlinear boundary value problems by combining the homotopy perturbation method and reproducing kernel Hilbert space method , 2010, Int. J. Comput. Math..

[15]  F. Stenger.  Handbook of Sinc Numerical Methods , 2010 .

[16]  Mohamed El-Gamel,et al.  Sinc-Galerkin method for solving nonlinear boundary-value problems , 2004 .

[17]  F. Stenger.  Numerical Methods Based on Whittaker Cardinal, or Sinc Functions , 1981 .

[18]  S. Ha.  A nonlinear shooting method for two-point boundary value problems , 2001 .

[19]  Frank Stenger,et al.  Whittaker's Cardinal Function in Retrospect* , 1971 .

[20]  Wei-Cheng Lian,et al.  Positive solution for singular boundary value problems , 1996 .

[21]  Jalil Rashidinia,et al.  Convergence of approximate solution of system of Fredholm integral equations , 2007 .

[22]  Frank Stenger.  A “sinc-Galerkin” method of solution of boundary value problems , 1979 .

[23]  Anne C. Morlet,et al.  Convergence of the sinc method for a fourth-order ordinary differential equation with an application , 1995 .

[24]  Frank Stenger,et al.  Sinc Methods for Quadrature and Differential Equations (J. Lund and K. L. Bowers) , 1993, SIAM Rev..

[25]  Mehdi Dehghan,et al.  The numerical solution of a nonlinear system of second-order boundary value problems using the sinc-collocation method , 2007, Math. Comput. Model..

[26]  Convergence of the Sinc method applied to Volterra integral equations , 2010 .