An Efficient Numerical Method for the Solution of the Schrödinger Equation

Abstract EN

The development of a new five-stage symmetric two-step fourteenth-algebraic order method with vanished phase-lag and its first, second, and third derivatives is presented in this paper for the first time in the literature.

More specifically we will study (1) the development of the new method, (2) the determination of the local truncation error (LTE) of the new method, (3) the local truncation error analysis which will be based on test equation which is the radial time independent Schrödinger equation, (4) the stability and the interval of periodicity analysis of the new developed method which will be based on a scalar test equation with frequency different than the frequency of the scalar test equation used for the phase-lag analysis, and (5) the efficiency of the new obtained method based on its application to the coupled Schrödinger equations.