Bi-Finite Difference Method to Solve Second-Order Nonlinear Hyperbolic Telegraph Equation in Two Dimensions

Abstract

This study introduces a computational scheme by the bi-finite difference method (Bi-FDM) to solve the hyperbolic telegraph equation in two dimensions. The proposed numerical method converts nonlinear two-dimensional hyperbolic telegraph equation of second order to difference equations that can be solved by the Mathematica program. Consistency and stability of the proposed scheme are discussed and found to be accurate of $O\left({\left(h_x\right)}^2+{\left(h_y\right)}^2+{\left(\mathrm{\Delta }\tau \right)}^2\right)$ and conditionally stable, respectively. The efficiency and accuracy of Bi-FDM have been shown by comparing the numerical results of the presented problems with the exact solutions and other numerical techniques.