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

摘要

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