An algorithm based on a new DQM with modified exponential cubic B-splines for solving hyperbolic telegraph equation in $(2+1)$ dimension

TL;DR

This paper introduces a novel modified exponential cubic B-spline differential quadrature method for efficiently solving the hyperbolic telegraph equation in two spatial dimensions, demonstrating its stability and accuracy through numerical comparisons.

Contribution

The paper presents a new differential quadrature method based on modified exponential cubic B-splines for space discretization of the hyperbolic telegraph equation, including stability analysis and numerical validation.

Findings

The method is conditionally stable based on eigenvalue analysis.

Numerical results show high accuracy with reduced errors.

The approach outperforms some existing numerical methods for the problem.

Abstract

This paper developed a method called "modified exponential cubic B-Spline differential quadrature (mExp-DQM) for space discretization together with a time integration algorithm" for the numerical computation of hyperbolic telegraph equation in $(2+1)$ dimension. The mExp-DQM is a new differential quadrature method based on modified exponential cubic B-splines as basis which reduces the problem into an amenable system of ordinary differential equations. The resulting system is solved using a time integration algorithm. The stability of the method is also studied by computing the eigenvalues of the coefficients matrices, it is found that the scheme is conditionally stable. The accuracy of the method is illustrated by computing the error between analytical solutions and numerical solutions is measured by using $L_2$ and $L_{\infty}$ error norms for each problem. A comparison of mExp-DQM solutions with the results of the other numerical methods has been carried out for various space sizes and time step sizes.