Eighth order methods for accurate computations for the Schrödinger equation Original Research Article

A family of new hybrid eighth algebraic order three-step methods with phase-lag of order 10(2) 18 is developed forcomputing elastic scattering phase shifts of the one-dimensional Schrödinger equation and for the numerical solution of coupled equations arising from the Schrödinger equation. Based on these new methods we obtain a new embedded variablestep procedure for the numerical integration of the Schrödinger equation. Numerical results obtained for the integration of the phase shift problem for the well-known case of the Lennard-Jones potential and for the integration of coupled Schrödinger equations show that these new methods are better than other finite difference methods.