Fourth-order energy-preserving time integrator for solving the sine-Gordon equation
摘要
In this paper, a fourth-order energy-preserving time integrator is derived by improving the classical average vector field integrator. Combining the proposed novel time integrator with the Fourier pseudo-spectral spatial discretisation, we develop and analyze an energy-preserving fully discrete scheme for the sine-Gordon equation with periodic boundary conditions. Numerical results verify the energy preservation and the accuracy of the proposed fully discrete scheme.