A hybrid method with phase-lag and derivatives equal to zero for the numerical integration of the Schrödinger equation

Abstract

A family of hybrid methods with algebraic order eight is proposed, with phase-lag and its first four derivatives eliminated. We investigate the behavior of the new algorithm and the property of the local truncation error and a comparison with other methods leads to conclusions and remarks about its accuracy and stability. The newly created method, as well as another Numerov-type methods, are applied to the resonance problem of the radial Schrodinger equation. The eigenenergies approximations, which are obtained prove the superiority of the new two-step method.