A new piecewise reproducing kernel function algorithm for solving nonlinear Hamiltonian systems

Abstract

This paper aims to study a new reproducing kernel (RK) function-based collocation method for nonlinear Hamiltonian systems. By applying the associated functions of RK spaces W2,02, W2,03 and W2,04, we propose the second, third and fourth-order schemes, respectively. Since the coefficient matrix of the linear system obtained by our scheme is symmetric and positive definite, our approach is uniquely solvable.The numerical experiments verify that our algorithms are efficient and can simulate the long time behavior including energy conservation and symplectic structure properties.