This work deals with differential quadrature method (DQ method) with a redefined form of quartic B-splines (In brief, mQB-DQ) for the simulating the time dependent partial differential equations. Specially telegraph equations are studied by implementing the proposed mQB-DQ for spatial domain and SSP-RK43 in temporal domain. In mQB-DQ method, the weighting coefficients for the spatial derivatives are evaluated using modified quartic B-splines as basis functions. The accuracy and effectiveness of the proposed method mQB-DQ is assessed via evaluating mQB-DQ solutions of some test examples of telegraph equation in terms of L2 and L errors and the convergence rate. Also the evaluated results depicted graphically. The mQB-DQ is shown the spatial accuracy of order four and produces conditionally stable solution for telegraph equation.

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