An algorithm based on a new DQM with modified extended cubic B-splines for numerical study of two dimensional hyperbolic telegraph equation

Abstract

In this paper, a new approach “modified extended cubic B-Spline differential quadrature (mECDQ) method” has been developed for the numerical computation of two dimensional hyperbolic telegraph equation. The mECDQ method is a DQM based on modified extended cubic B-spline functions as new base functions. The mECDQ method reduces the hyperbolic telegraph equation into an amenable system of ordinary differential equations (ODEs), in time. The resulting system of ODEs has been solved by adopting an optimal five stage fourth-order strong stability preserving Runge - Kutta (SSP-RK54) scheme. The stability of the method is also studied by computing the eigenvalues of the coefficient matrices. It is shown that the mECDQ method produces stable solution for the telegraph equation. The accuracy of the method is illustrated by computing the errors between analytical solutions and numerical solutions are measured in terms of L2 and L∞ and average error norms for each problem. A comparison of mECDQ solutions with the results of the other numerical methods has been carried out for various space sizes and time step sizes, which shows that the mECDQ solutions are converging very fast in comparison with the various existing schemes.