Sinc-Galerkin method for numerical solution of the Bratu's problems

Authors:
Jalil Rashidinia;Khosro Maleknejad;Narges Taheri
Affiliations:
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran;Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran;Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran
Venue:
Numerical Algorithms
Year:
2013

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Abstract

Study of the performance of the Galerkin method using sinc basis functions for solving Bratu's problem is presented. Error analysis of the presented method is given. The method is applied to two test examples. By considering the maximum absolute errors in the solutions at the sinc grid points are tabulated in tables for different choices of step size. We conclude that the Sinc-Galerkin method converges to the exact solution rapidly, with order, $O(\exp{(-c \sqrt{n}}))$ accuracy, where c is independent of n.