Numerical solution of hyperbolic telegraph equation using the Chebyshev tau method

Abstract

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.

Systems of nonlinear Volterra integro-differential equations of arbitrary order

“…Some of Chebyshev polynomials properties are: orthogonality, recursive, real zeros, complete for the space of polynomials, etc. For these reasons, many researchers have employed these polynomials in their research [17,18,19,20,21,22,23].…”

Comparison of Adomian Decomposition Method and Taylor Matrix Method in Solving Different Kinds of Partial Differential Equations

“…Mohebbi and Dehaghan [15], studied high order compact solution to solve the telegraph equation. Saadatmandi and Dehaghan [16], developed a numerical solution based on Chebyshev Tau method. Yousefi [17] used Legendre multi wavelet Galerkin method for solving the hyperbolic telegraph equation.…”

A Collocation Method for Numerical Solution of Hyperbolic Telegraph Equation with Neumann Boundary Conditions

“…Unconditionally stable finite difference schemes have been proposed in [9,10]. Dehghan and Lakestani [11] used the Chebyshev cardinal functions, whereas Saadatmandi and Dehghan [12] used the Chebyshev tau method for expanding the approximate solution of one-dimensional telegraph equation. Mohebbi and Dehghan [13] reported a higher order compact finite difference approximation of fourth order in space and used collocation method for time direction.…”