Study of One Dimensional Hyperbolic Telegraph Equation Via a Hybrid Cubic B-Spline Differential Quadrature Method

Abstract

Hybrid cubic B-spline differential quadrature method (in brief, HCB-DQM) have been proposed for the study of one space dimensional time dependent partial differential equations. Specially, we have applied the proposed method for 1D telegraph equation (1D TE). The HCB-DQM is based on DQM with hybrid cubic-B-splines as base functions, and so, the 1D TE is reduced to a system of first order ordinary differential equations (ODEs) which is solved via SSP-RK43 scheme. The accurateness and efficiency of the proposed method is tested for four examples of 1D TE via $$L_2$$ L 2 and $$L_\\infty $$ L ∞ errors. It is demonstrated that proposed HCB-DQM produces stable solutions for 1D telegraph equation. The evaluated solutions are compared with the exact results. Also, we compare the evaluated results with existing recently published results. It is seen that the produced results are agreed well with the exact solutions. Easy to implementation, economically and straightforwardness is main advantage of HCB-DQM.