Abstract
In this work we propose a high-order and accurate method for solving the one-dimensional nonlinear sine–Gordon equation. The proposed method is based on applying a compact finite difference scheme and the diagonally implicit Runge–Kutta–Nyström (DIRKN) method for spatial and temporal components, respectively. We apply a compact finite difference approximation of fourth order for discretizing the spatial derivative and a fourth-order A -stable DIRKN method for the time integration of the resulting nonlinear second-order system of ordinary differential equations. The proposed method has fourth-order accuracy in both space and time variables and is unconditionally stable. The results of numerical experiments show that the combination of a compact finite difference approximation of fourth order and a fourth-order A -stable DIRKN method gives an efficient algorithm for solving the one-dimensional sine–Gordon equation.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
