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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 686483, 10 pages
http://dx.doi.org/10.1155/2013/686483
Research Article

Numerical Solution and Simulation of Second-Order Parabolic PDEs with Sinc-Galerkin Method Using Maple

Department of Mathematical Engineering, Yildiz Technical University, Davutpasa, 34210 Istanbul, Turkey

Received 4 March 2013; Accepted 12 June 2013

Academic Editor: Adem Kılıçman

Copyright © 2013 Aydin Secer. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

An efficient solution algorithm for sinc-Galerkin method has been presented for obtaining numerical solution of PDEs with Dirichlet-type boundary conditions by using Maple Computer Algebra System. The method is based on Whittaker cardinal function and uses approximating basis functions and their appropriate derivatives. In this work, PDEs have been converted to algebraic equation systems with new accurate explicit approximations of inner products without the need to calculate any numeric integrals. The solution of this system of algebraic equations has been reduced to the solution of a matrix equation system via Maple. The accuracy of the solutions has been compared with the exact solutions of the test problem. Computational results indicate that the technique presented in this study is valid for linear partial differential equations with various types of boundary conditions.