Application of polynomial scaling functions for numerical solution of telegraph equation

Abstract

In this paper, we present a numerical method based on the polynomial scaling functions to solve the second-order one-space-dimensional hyperbolic telegraph equation. The method consists of expanding the approximate solution as the elements of polynomial scaling functions. The operational matrix of derivative for polynomial scaling functions is developed. Using the operational matrix of derivative, the problem reduces to a set of algebraic linear equations. An estimation of error bound for this method is investigated. Two numerical examples are included to demonstrate the validity and applicability of the technique. The method is easy to implement and produces considerable accurate results among the existing scaling functions.

Keywords:

• telegraph equation
• polynomial scaling functions
• operational matrix of derivative
• convergence analysis

AMS Subject Classifications:

• 65T60
• 35L20
• 65L60
• 32E30

Acknowledgements

The authors would like to thank the reviewers for their valuable suggestions which greatly improved the standard of the paper.