Numerical solution of the hyperbolic telegraph equation using cubic B-spline-based differential quadrature of high accuracy

By constructing a newly modified cubic B-splines having the optimal accuracy order four, we propose a numerical scheme for solving the hyperbolic telegraph equation using a differential quadrature method. The spatial derivatives are approximated by the differential quadrature whose weight coefficients are computed using the newly modified cubic B-splines. Our modified cubic B-splines retain the tridiagonal structure and achieve the fourth order convergence rate. The solution of the associated ODEs is advanced in the time domain by the SSPRK scheme. The stability of the method is analyzed using the discretization matrix. Our numerical experiments demonstrate the better performance of our proposed scheme over several known numerical schemes reported in the literature.

Keywords:

Hyperbolic telegraph equation , Differential quadrature method , SSPRK scheme , Modified cubic B-spline basis functions , Discretization matrix