High Order Energy Preserving Composition Method for Multi-Symplectic Sine-Gordon Equation

Jianqiang Sun (), Jingxian Zhang and Jiameng Kong
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Jianqiang Sun: Department of Mathematics, School of Science, Hainan University, Haikou 570228, China
Jingxian Zhang: Department of Mathematics, School of Science, Hainan University, Haikou 570228, China
Jiameng Kong: Department of Mathematics, School of Science, Hainan University, Haikou 570228, China

Mathematics, 2023, vol. 11, issue 5, 1-19

Abstract: A fourth-order energy preserving composition scheme for multi-symplectic structure partial differential equations have been proposed. The accuracy and energy conservation properties of the new scheme were verified. The new scheme is applied to solve the multi-symplectic sine-Gordon equation with periodic boundary conditions and compared with the corresponding second-order average vector field scheme and the second-order Preissmann scheme. The numerical experiments show that the new scheme has fourth-order accuracy and can preserve the energy conservation properties well.

Keywords: average vector field method; multi-symplectic structure; Fourier pseudo-spectral method; sine-Gordon equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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