New high order multiderivative explicit four-step methods with vanished phase-lag and its derivatives for the approximate solution of the Schrödinger equation. Part I: Construction and theoretical analysis

2012 ◽  
Vol 51 (1) ◽  
pp. 194-226 ◽  
Author(s):  
T. E. Simos
Keyword(s):  
Approximate Solution ◽  
Theoretical Analysis ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
High Order ◽  
Phase Lag

Optimizing a class of linear multi-step methods for the approximate solution of the radial Schrödinger equation and related problems with respect to phase-lag

Open Physics ◽  
2011 ◽  
Vol 9 (6) ◽  
Author(s):  
Theodore Simos
Keyword(s):  
Approximate Solution ◽  
Schrödinger Equation ◽  
Numerical Method ◽  
Schrodinger Equation ◽  
Phase Lag ◽  
Radial Schrödinger Equation ◽  
Multi Step Methods

AbstractIn this paper we consider a methodology of optimization of the efficiency of a numerical method for the approximate solution of the radial Schrödinger equation and related problems. More specifically, we show how the methodology of vanishing of the phase-lag and its derivatives optimizes the behaviour of a numerical method.

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