Abstract and Applied Analysis

New Spectral Second Kind Chebyshev Wavelets Algorithm for Solving Linear and Nonlinear Second-Order Differential Equations Involving Singular and Bratu Type Equations

W. M. Abd-Elhameed, E. H. Doha, and Y. H. Youssri

Full-text: Open access

Abstract

A new spectral algorithm based on shifted second kind Chebyshev wavelets operational matrices of derivatives is introduced and used for solving linear and nonlinear second-order two-point boundary value problems. The main idea for obtaining spectral numerical solutions for these equations is essentially developed by reducing the linear or nonlinear equations with their initial and/or boundary conditions to a system of linear or nonlinear algebraic equations in the unknown expansion coefficients. Convergence analysis and some efficient specific illustrative examples including singular and Bratu type equations are considered to demonstrate the validity and the applicability of the method. Numerical results obtained are compared favorably with the analytical known solutions.

Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 715756, 9 pages.

Dates
First available in Project Euclid: 27 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393512178

Digital Object Identifier
doi:10.1155/2013/715756

Mathematical Reviews number (MathSciNet)
MR3134179

Zentralblatt MATH identifier
07095271

Citation

Abd-Elhameed, W. M.; Doha, E. H.; Youssri, Y. H. New Spectral Second Kind Chebyshev Wavelets Algorithm for Solving Linear and Nonlinear Second-Order Differential Equations Involving Singular and Bratu Type Equations. Abstr. Appl. Anal. 2013 (2013), Article ID 715756, 9 pages. doi:10.1155/2013/715756. https://projecteuclid.org/euclid.aaa/1393512178


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References

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