8TH ORDER METHODS WITH MINIMAL PHASE-LAG FOR ACCURATE COMPUTATIONS FOR THE ELASTIC-SCATTERING PHASE-SHIFT PROBLEM

Two new hybrid eighth algebraic order two-step methods with phase-lag of order twelve and fourteen are developed for computing elastic scatt ering phase shifts of the radial Schrodinger equation. Based on these new methods we obtain a new variable-step procedure for the numerical integration of the Schrodinger equation. Numerical results obtained fo r the integration of the phase shift problem for the well known case o f the Lennard-Jones potential show that these new methods are better t han other finite difference methods.