New Tchebyshev‐Galerkin operational matrix method for solving linear and nonlinear hyperbolic telegraph type equations. Issue 6 (28th June 2016)

• Record Type: Journal Article
• Authors: Abd‐Elhameed, W. M.; Doha, E. H.; Youssri, Y. H.; Bassuony, M. A.
• Is Part Of: Numerical methods for partial differential equations. Volume 32:Issue 6(2016:Nov.)
• Page Start: 1553
• Page End: 1571
• Publication Date: 2016-06-28
• Subjects: Chebyshev polynomials -- Galerkin and collocation methods -- hyperbolic telegraph equation -- operational matrix; Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.22074
• Languages: English
• ISSNs: 0749-159X

Abstract

Abstract : 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