New Tchebyshev-Galerkin operational matrix method for solving linear and nonlinear hyperbolic telegraph type equations

The telegraph equation describes various phenomena in many applied sciences. We propose two new efficient spectral algorithms for handling this equation. The principal idea behind these algorithms is to convert the linear/nonlinear telegraph problems (with their initial and boundary conditions) into...

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Bibliographic Details
Published in:Numerical methods for partial differential equations 2016-11, Vol.32 (6), p.1553-1571
Main Authors: Abd-Elhameed, W. M., Doha, E. H., Youssri, Y. H., Bassuony, M. A.
Format: Article
Language:English
Subjects:
Algorithms
Chebyshev polynomials
Convergence
Galerkin and collocation methods
hyperbolic telegraph equation
Linear systems
Mathematical analysis
Mathematical models
Nonlinearity
Numerical analysis
operational matrix
Spectra
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Summary:The telegraph equation describes various phenomena in many applied sciences. We propose two new efficient spectral algorithms for handling this equation. The principal idea behind these algorithms is to convert the linear/nonlinear telegraph problems (with their initial and boundary conditions) into a system of linear/nonlinear equations in the expansion coefficients, which can be efficiently solved. The main advantage of our algorithm in the linear case is that the resulting linear systems have special structures that reduce the computational effort required for solving them. The numerical algorithms are supported by a careful convergence analysis for the suggested Chebyshev expansion. Some illustrative examples are given to demonstrate the wide applicability and high accuracy of the proposed algorithms. © 2016Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 1553–1571, 2016
ISSN:0749-159X
1098-2426
DOI:10.1002/num.22074