Explicit high-order energy-preserving methods for general Hamiltonian partial differential equations

A novel class of explicit high-order energy-preserving methods are proposed for general Hamiltonian partial differential equations with non-canonical structure matrix. When the energy is not quadratic, it firstly done that original system reformulated into an equivalent form a modified quadratic conservation law by quadratization approach. Then resulting satisfies discretized in time combining Runge–Kutta orthogonal projection techniques. The schemes shown to share order method and thus can reach desired accuracy. Moreover, because step be solved explicitly. Numerical results addressed demonstrate remarkable superiority comparison other structure-preserving methods.