Two new phase-fitted symplectic partitioned Runge-Kutta methods

摘要

New symplectic Partitioned Runge-Kutta (SPRK) methods with phase-lag of order infinity are derived in this paper. Specifically two new symplectic methods are constructed with second and third algebraic order. The methods are tested on the numerical integration of Hamiltonian problems and on the estimation of the eigenvalues of the Schr?dinger equation.