Abstract and Applied Analysis

Spectral Shifted Jacobi Tau and Collocation Methods for Solving Fifth-Order Boundary Value Problems

A. H. Bhrawy, A. S. Alofi, and S. I. El-Soubhy

Full-text: Open access

Abstract

We have presented an efficient spectral algorithm based on shifted Jacobi tau method of linear fifth-order two-point boundary value problems (BVPs). An approach that is implementing the shifted Jacobi tau method in combination with the shifted Jacobi collocation technique is introduced for the numerical solution of fifth-order differential equations with variable coefficients. The main characteristic behind this approach is that it reduces such problems to those of solving a system of algebraic equations which greatly simplify the problem. Shifted Jacobi collocation method is developed for solving nonlinear fifth-order BVPs. Numerical examples are performed to show the validity and applicability of the techniques. A comparison has been made with the existing results. The method is easy to implement and gives very accurate results.

Article information

Source
Abstr. Appl. Anal., Volume 2011 (2011), Article ID 823273, 14 pages.

Dates
First available in Project Euclid: 12 August 2011

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1313171209

Digital Object Identifier
doi:10.1155/2011/823273

Mathematical Reviews number (MathSciNet)
MR2817267

Zentralblatt MATH identifier
1221.65171

Citation

Bhrawy, A. H.; Alofi, A. S.; El-Soubhy, S. I. Spectral Shifted Jacobi Tau and Collocation Methods for Solving Fifth-Order Boundary Value Problems. Abstr. Appl. Anal. 2011 (2011), Article ID 823273, 14 pages. doi:10.1155/2011/823273. https://projecteuclid.org/euclid.aaa/1313171209


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