Numerical solution of nonlinear sine–Gordon equation by using the modified cubic B-spline differential quadrature method

Publication date: Available online 13 December 2016Source: Beni-Suef University Journal of Basic and Applied SciencesAuthor(s): H.S. Shukla, Mohammad TamsirAbstractThis paper deals with numerical solution of one dimensional nonlinear sine–Gordon. “Modified cubic B-spline differential quadrature method” is used to solve one dimensional nonlinear sine–Gordon. The method reduces the problem to a system of first order ordinary differential equations (ODEs). The resulting system of ODEs is solved by “an optimal five stage and fourth-order strong stability preserving Runge–Kutta (SSP-RK54) method”. Finally, the method is illustrated and compared with existing methods via numerical examples. It is found that the method not only is quite easy to implement, but also gives better results than the ones already existing in the literature.

Source: Beni Suef University Journal of Basic and Applied Sciences - July 11, 2018 Category: Science Source Type: research