Abstract
AbstractIn this article, a modified cubic B-spline differential quadrature method (MCB-DQM) is proposed to solve some of the basic differential equations. Here we have considered an ordinary differential equation of order two along with heat equation and one- and two-dimensional wave equations. A nonlinear ordinary differential equation of order two is also considered. The ordinary differential equation is reduced to a system of nonhomogeneous linear equations which is then solved by using the Gauss elimination method, whereas the heat equation and the one-dimensional and two-dimensional heat and wave equations are reduced to a system of ordinary differential equations. The system is then solved by the optimal four-stage three-order strong stability preserving time stepping Runge–Kutta (SSP-RK43) scheme. The reliability and efficiency of the method have been tested on six examples.KeywordsOrdinary differential equationHeat equationWave equation cubic B-spline functionsModified cubic B-spline quadrature methodSystem of ordinary differential equationsGauss elimination methodRunge–Kutta fourth-order method
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