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Numerical solution of hyperbolic telegraph equation using the Chebyshev tau method
Author(s) -
Saadatmandi Abbas,
Dehghan Mehdi
Publication year - 2010
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.20442
Subject(s) - mathematics , chebyshev equation , telegrapher's equations , hyperbolic partial differential equation , chebyshev polynomials , algebraic equation , chebyshev iteration , scheme (mathematics) , partial differential equation , chebyshev filter , numerical analysis , derivative (finance) , mathematical analysis , chebyshev nodes , orthogonal polynomials , classical orthogonal polynomials , computer science , nonlinear system , telecommunications , physics , transmission line , quantum mechanics , financial economics , economics
In this article we propose a numerical scheme to solve the one‐dimensional hyperbolic telegraph equation. The method consists of expanding the required approximate solution as the elements of shifted Chebyshev polynomials. Using the operational matrices of integral and derivative, we reduce the problem to a set of linear algebraic equations. Some numerical examples are included to demonstrate the validity and applicability of the technique. The method is easy to implement and produces very accurate results. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010