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New Tchebyshev‐Galerkin operational matrix method for solving linear and nonlinear hyperbolic telegraph type equations
Author(s) -
AbdElhameed W. M.,
Doha E. H.,
Youssri Y. H.,
Bassuony M. A.
Publication year - 2016
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22074
Subject(s) - mathematics , nonlinear system , telegrapher's equations , chebyshev filter , partial differential equation , convergence (economics) , matrix (chemical analysis) , galerkin method , linear system , algorithm , mathematical analysis , computer science , telecommunications , physics , materials science , transmission line , quantum mechanics , economics , composite material , economic growth
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