A predictor–corrector explicit four-step method with vanished phase-lag and its first, second and third derivatives for the numerical integration of the Schrödinger equation

Abstract

A predictor–corrector explicit four-step method of sixth algebraic order is investigated in this paper. More specifically, we investigate the results of the elimination of the phase-lag and its first, second and third derivatives on the efficiency of the proposed method. The resultant method is studied theoretically and computationally. The theoretical investigation of the new hybrid method consists of: (1) the construction of the new method, (2) the definition (calculation) of the local truncation error, (3) the comparative local truncation error analysis (with other known methods of the same form), (4) the stability analysis using scalar test equation with frequency different than the frequency of the phase-lag analysis. Finally, we will study computationally the new obtained method. This study is based on the application of the new produced predictor–corrector explicit four-step method to the approximate solution of the resonance problem of the radial time independent Schrodinger equation.