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Abstract and Applied Analysis
Volume 2013, Article ID 542839, 9 pages
Research Article

New Wavelets Collocation Method for Solving Second-Order Multipoint Boundary Value Problems Using Chebyshev Polynomials of Third and Fourth Kinds

1Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia
2Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt

Received 7 August 2013; Revised 13 September 2013; Accepted 13 September 2013

Academic Editor: Soheil Salahshour

Copyright © 2013 W. M. Abd-Elhameed et al. 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.


This paper is concerned with introducing two wavelets collocation algorithms for solving linear and nonlinear multipoint boundary value problems. The principal idea for obtaining spectral numerical solutions for such equations is employing third- and fourth-kind Chebyshev wavelets along with the spectral collocation method to transform the differential equation with its boundary conditions to a system of linear or nonlinear algebraic equations in the unknown expansion coefficients which can be efficiently solved. Convergence analysis and some specific numerical examples are discussed to demonstrate the validity and applicability of the proposed algorithms. The obtained numerical results are comparing favorably with the analytical known solutions.