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### Comparison of Numerical Solution of 1D Hyperbolic Telegraph Equation using B-Spline and Trigonometric B-Spline by Differential Quadrature Method

#### Abstract

Objectives: This paper aims to compute the approximate solution of one dimensional (1D) hyperbolic telegraph equation with appropriate primary and limiting conditions. Methods/Statistical Analysis: To find the approximate solution, two different modified spline basis function are used with the differential quadrature method and splines are used to compute the weighting coefficients and thus the equation is transformed to a set of first order conventional differential equations which is further solved by the SSP-RK43 method. Three test problems of this equation are simulated to establish the precision and usefulness of the proposed scheme. Findings: The obtained numerical results are found to be good in terms of accuracy, efficiency and simplicity. To validate the computed results using proposed scheme, various comparisons at different time levels has been done in the form of and errors. These errors are compared and enlisted in the form of tables with computed errors enlisted in literature. Application/Improvements: Being an important equation of nuclear material science, one dimensional (1D) hyperbolic telegraphs equation needs to take care in the sense of better numerical solution. In this context, a successful effort has been done in this research article by proposing a hybrid numerical scheme.

#### Keywords

35K57, Differential Quadrature Method, Hyperbolic Telegraphs Equation, Mathematics Subject Classification (2010): 65M06, Modified Cubic B-Spline, Modified Trigonometric B-Spline, SSP-RK43.

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