A collocation method for numerical solution of Telegraph equation

TL;DR

This paper introduces a B-spline collocation method for solving the one-dimensional telegraph equation, demonstrating its convergence and efficiency through numerical tests compared to analytical solutions.

Contribution

The paper develops and proves the convergence of a novel B-spline collocation approach for the telegraph equation, with validation via numerical experiments.

Findings

The method converges for the telegraph equation.

Numerical results align well with analytical solutions.

The approach is computationally efficient.

Abstract

In this paper, B-spline collocation method is developed for the solution of one-dimensional hyperbolic telegraph equation. The convergence of the method is proved. Also the method is applied on some test examples, and the numerical results have been compared with the analytical solutions. The $L_\infty$,$L_2$ and Root-Mean-Square errors (RMS) in the solutions show the efficiency of the method computationally.