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2014 An Efficient Numerical Approach for Solving Nonlinear Coupled Hyperbolic Partial Differential Equations with Nonlocal Conditions
A. H. Bhrawy, M. A. Alghamdi, Eman S. Alaidarous
Abstr. Appl. Anal. 2014: 1-14 (2014). DOI: 10.1155/2014/295936

Abstract

One of the most important advantages of collocation method is the possibility of dealing with nonlinear partial differential equations (PDEs) as well as PDEs with variable coefficients. A numerical solution based on a Jacobi collocation method is extended to solve nonlinear coupled hyperbolic PDEs with variable coefficients subject to initial-boundary nonlocal conservation conditions. This approach, based on Jacobi polynomials and Gauss-Lobatto quadrature integration, reduces solving the nonlinear coupled hyperbolic PDEs with variable coefficients to a system of nonlinear ordinary differential equation which is far easier to solve. In fact, we deal with initial-boundary coupled hyperbolic PDEs with variable coefficients as well as initial-nonlocal conditions. Using triangular, soliton, and exponential-triangular solutions as exact solutions, the obtained results show that the proposed numerical algorithm is efficient and very accurate.

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A. H. Bhrawy. M. A. Alghamdi. Eman S. Alaidarous. "An Efficient Numerical Approach for Solving Nonlinear Coupled Hyperbolic Partial Differential Equations with Nonlocal Conditions." Abstr. Appl. Anal. 2014 1 - 14, 2014. https://doi.org/10.1155/2014/295936

Information

Published: 2014
First available in Project Euclid: 2 October 2014

zbMATH: 07022111
MathSciNet: MR3198171
Digital Object Identifier: 10.1155/2014/295936

Rights: Copyright © 2014 Hindawi

Vol.2014 • 2014
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