Some Difference Algorithms for Nonlinear Klein-Gordon Equations
In this study, sixth and eighth-order finite difference schemes combined with a third-order strong stability preserving Runge-Kutta (SSP-RK3) method are employed to cope with the nonlinear Klein-Gordon equation, which is one of the important mathematical models in quantum mechanics, without any linearization or transformation. Various numerical experiments are examined to verify the applicability and efficiency of the proposed schemes. The results indicate that the corresponding schemes are seen to be reliable and effectively applicable. Another salient feature of these algorithms is that they achieve high-order accuracy with relatively less number of grid points. Therefore, these schemes are realized to be a good option in dealing with similar processes represented by partial differential equations.
KeywordsKlein-Gordon equation Nonlinear processes High-order finite difference scheme Strong stability preserving Runge-Kutta
- 12.Sarboland, M., Aminataei, A.: Numerical solution of the nonlinear Klein-Gordon equation using multiquadratic quasi-interpolation scheme. Univ. J. Appl. Math. 3, 40–49 (2015)Google Scholar