A Family of Implicit Six-Step Methods with Vanished Phase-Lag and its Derivatives for the Numerical Solution of the Schr?dinger Equation and Related Problems

摘要

A family of implicit symmetric linear six-step methods for the numerical solution of second order periodic initial or boundary-value problems is investigated in this paper. The construction of the new family of methods is based on: ? the vanishing phase-lag and ? the vanished of its derivatives. For the produced methods of the new family of methods, we investigate their local truncation error and its application to a test problem. We compare the results of the above mentioned application in order to extract summaries about the efficiency of each method of the family. We also studied the stability for the developed methods of the new family of methods. Finally, we applied the new produced family of methods to the resonance problem of the radial time independent Schrodinger equation in order to show their efficiency.