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Mathematical Problems in Engineering
Volume 2014, Article ID 369029, 6 pages
Research Article

An Efficient Spectral Approximation for Solving Several Types of Parabolic PDEs with Nonlocal Boundary Conditions

1Department of Mathematics, Aligoudarz Branch, Islamic Azad University, Aligoudarz, Iran
2Department of Mathematics, Institute for Mathematical Research, Universiti Putra Malaysia, UPM, 43400 Serdang, Selangor, Malaysia

Received 30 December 2013; Accepted 28 January 2014; Published 9 March 2014

Academic Editor: Yuji Liu

Copyright © 2014 E. Tohidi and A. Kılıçman. 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.


The problem of solving several types of one-dimensional parabolic partial differential equations (PDEs) subject to the given initial and nonlocal boundary conditions is considered. The main idea is based on direct collocation and transforming the considered PDEs into their associated algebraic equations. After approximating the solution in the Legendre matrix form, we use Legendre operational matrix of differentiation for representing the mentioned algebraic equations clearly. Three numerical illustrations are provided to show the accuracy of the presented scheme. High accurate results with respect to the Bernstein Tau technique and Sinc collocation method confirm this accuracy.