A Modification on The Exponential Cubic B-spline for Numerical Simulation of Hyperbolic Telegraph Equations

In this paper the differential quadrature method is implemented to find numerical solution of two and three-dimensional telegraphic equations with Dirichlet and Neumann's boundary values. This technique is according to exponential cubic B-spline functions. So, a modification on the exponential cubic B- spline is applied in order to use as a basis function in the DQ method. Therefore, the Telegraph equation (TE) is altered to a system of ordinary differential equations (ODEs). The optimized form of Runge-Kutta scheme has been implemented by four-stage and three-order strong stability preserving (SSPRK۴۳) to solve the resulting system of ODEs. We examined the correctness and applicability of this method by four examples of the TE.

Keywords:

Telegraph equation (TE) , Exponential modified , Cubic B-spline function , SSP-RK۴۳ , Differential. quadrature method