Energy Preserving Method Of Multi-symplectic Partial Differential Equation

Nonlinear phenomena is a common dynamic behavior in applied mathematics and physics.It can be described by many coupled partial differential equations,such as strongly coupled schrodingerequation,RLW equation,Dirac equation and CNLS equat-ion.The system which described by these coupled PDEs have energy conservation properties.Hamiltonian system with energy conservation properties is used widely to describe various physical phenomena,and the system is a great significance in nature.In recent years,numerical algorithm for the specific structural characteristics of the PDEs has become an important part of computational mathematics.In this paper,we use the average vector field method and Fourier pseudo-spectral method to construct the high-order guaranteed energy format of coupled partial differential equations.The new format of the equation is numerically simulated and its numerical results are analyzed.Energy-preserving algorithn is an important research direction of structure preserving algorithm.In this paper,the average vector field method and Fourier pseudospectral method are used to construct high-order energy-preserving schemes for coupled partial differential equations.The new schemes are nunerically simulated and their numerical results are analyzed.The numerical experiments show that the new schemes are effective and have advantages in energy conservation.