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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.

In this work, collocation method based on B-SPLINE functions is used to obtained a numerical solution for one-dimensional HYPERBOLIC telegraph equation. The proposed method is consists of two main steps. As , rst step, by using , nite di, erence scheme for time variable, partial di, erential equation is converted to an ordinary di, erential equation by space variable. In the next step, for solving this equation collocation method is used. In the analysis section of the proposed method, the convergence of the method is studied. Also, some numerical results are given to demonstrate the validity and applicability of the presented technique. The L1, L2 and Root-Mean-Square(RMS) in the solutions show the e, ciency of the method computationally.

In this paper, a numerical method is developed for solving a linear sixth order boundary value problem (6VBP) by using the HYPERBOLIC uniform SPLINE of order 3 (lower order). There is proved to be first-order convergent. Numerical results confirm the order of convergence predicted by the analysis.