The use of Chebyshev cardinal functions for solution of the second‐order one‐dimensional telegraph equation

Abstract

A numerical technique is presented for the solution of the second order one-dimensional linear hyperbolic equation. This method uses the Chebyshev cardinal functions. The method consists of expanding the required approximate solution as the elements of Chebyshev cardinal functions. Using the operational matrix of derivative, the problem is reduced to a set of 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.

A Numerical Study of One-Dimensional Hyperbolic Telegraph Equation

“…. The exact solution by [2,34] is , cos sin (19) This problem was solved by HAM in [10]. For q-HAM solution we choose the linear operator:…”

“…Also the propagation of acoustic waves in Darcy-type porous media [35], and parallel flows of viscous Maxwell fluids [1] are just some of the phenomena governed [8,19] by Eq.(1). In [2], a numerical scheme for solving the secondorder one-space-dimensional linear hyperbolic equation has been presented by using the shifted Chebyshev cardinal functions. Dehghan and Shokri [3,4] have studied a numerical scheme to solve one and two-dimensional hyperbolic equations using collocation points and the thin-plate-spline radial basis functions.…”

A New Semi-Analytical Solution of the Telegraph Equation with Integral Condition

“…The exact solution of this problem is v(x,t) = cost sin x [17,26,27]. For this problem, we obtain F(x,t) = 4 sin x(cost − 3 sint) − 3(2πx − π 2 + 4) 2π cost…”

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.…”