Two New Energy-preserving Algorithms For Generalized Fifth-order KdV Equation

Some partial differential equations (PDEs), for instance the sine-Gordon e-quation, the nonlinear Schrodinger equation, the Korteweg-de Vries equation, the Maxwell’s equations, the nonlinear wave equation and so on, can be written as a multi-symplectic Hamiltonian system, which has three local conservation laws, name-ly multi-symplectic conservation law, local energy conservation law and local momen-tum conservation law. It is very significant to construct the numerical methods that preserve some of the above conservation laws.In this thesis, based on the multi-symplectic formulations of the generalized fifth-order KdV equation and the averaged vector field method, two new energy-preserving methods are proposed, including a new local energy-preserving algorithm which is independent of the boundary conditions and a new global energy-preserving method. We prove that the proposed methods preserve the energy conservation laws exactly. Numerical experiments are carried out, which demonstrate that the numerical methods proposed in the thesis preserve energy well.