Numerical Study of Nonlinear sine-Gordon Equation by using the Modified Cubic B-Spline Differential Quadrature Method
This is an incremental contribution for researchers in numerical methods for partial differential equations, offering a variant of existing techniques.
The paper presents a numerical method combining modified cubic B-spline differential quadrature with a Runge-Kutta scheme to solve the nonlinear sine-Gordon equation, demonstrating accuracy through three test cases with exact solutions.
In this article, we study the numerical solution of the one dimensional nonlinear sine-Gordon by using the modified cubic B-spline differential quadrature method. 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. 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.