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In this article, we study the numerical solution of the one dimensionalnonlinear sine-Gordon by using the modified cubic B-spline differentialquadrature method. The scheme is a combination of a modified cubic B splinebasis function and the differential quadrature method. The modified cubic Bspline is used as a basis function in the differential quadrature method tocompute the weighting coefficients. Thus, the sine Gordon equation is convertedinto a system of ordinary differential equations (ODEs). The resulting systemof ODEs is solved by an optimal five stage and fourth order strong stabilitypreserving Runge Kutta scheme. The accuracy and efficiency of the scheme aresuccessfully described by considering the three numerical examples of thenonlinear sine Gordon equation having the exact solutions.

Numerical Study of Nonlinear sine-Gordon Equation by using the Modified Cubic B-Spline Differential Quadrature Method