Numerical Study of Nonlinear sine-Gordon Equation by using the Modified Cubic B-Spline Differential Quadrature Method
نویسندگان
چکیده
In this article, we study the numerical solution of the one dimensional nonlinear sineGordon by using the modified cubic B-spline differential quadrature method (MCB-DQM). The scheme is a combination of a modified cubic B-spline basis function and the differential quadrature method. The modified cubic B-spline is used as a basis function in the differential quadrature method to compute the weighting coefficients. Thus, the sine-Gordon equation is converted into a system of ordinary differential equations (ODEs). The resulting system of ODEs is solved by an optimal five stage and fourth-order strong stability preserving Runge– Kutta scheme (SSP-RK54). The accuracy and efficiency of the scheme are successfully described by considering the three numerical examples of the nonlinear sine-Gordon equation having the exact solutions.
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