An Efficient Spectral Approximation for Solving Several Types of Parabolic PDEs with Nonlocal Boundary Conditions. (9th March 2014)

• Record Type: Journal Article
• Authors: Tohidi, E.; Kılıçman, A.
• Other Names: Liu Yuji Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2014(2014)
• Publication Date: 2014-03-09
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2014/369029
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : 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.