A family of trigonometrically fitted partitioned Runge–Kutta symplectic methods

We are presenting a family of trigonometrically fitted partitioned Runge–Kutta symplectic methods of fourth order with six stages. The solution of the one-dimensional time independent Schrödinger equation is considered by trigonometrically fitted symplectic integrators. The Schrödinger equation is first transformed into a Hamiltonian canonical equation. Numerical results are obtained for the one-dimensional harmonic oscillator and the exponential potential.