Diagonally implicit trigonometrically fitted symplectic Runge–Kutta methods

The numerical integration of Hamiltonian systems with oscillatory or periodic solution is considered in this paper. The general framework of constructing trigonometrically fitted symplectic diagonally implicit Runge–Kutta methods is given. A trigonometrically fitted symplectic fourth algebraic order method is constructed. The method is applied to the numerical integration of Hamiltonian systems as the harmonic oscillator, the pendulum and the two body problem and the computation of the eigenvalues of the Schrödinger equation.