Abstract
A novel category of explicit conservative numerical methods with arbitrarily high-order is introduced for solving the nonlinear fractional Schrödinger wave equations in one and two dimensions. The proposed method is based on the scalar auxiliary variable approach. The equations studied is first transformed into an equivalent system by introducing a scalar auxiliary variable, and the energy is then reformulated as a sum of three quadratic terms. Applying the explicit relaxation Runge–Kutta methods in temporal and the Fourier pseudo-spectral discretization in spatial, the resulting time–space full discrete scheme is proved to preserve the reformulated energy in the discrete level to machine accuracy. The proposed methods improve the numerical stability during long-term computations, as demonstrated through numerical experiments. Also this idea can be easily extended to other similar equations, such as the nonlinear fractional wave equation and the fractional Klein–Gordon–Schrödinger equation.
Published Version
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.
