Some embedded modified Runge-Kutta methods for the numerical solution of some specific Schrödinger equations. (English) Zbl 0915.65084
A new embedded modified Runge-Kutta 4(6) Fehlberg method with minimal phase-lag and a block embedded Runge-Kutta-Fehlberg method are developed for the numerical solution of the Schrödinger equation \(y''(x)=[ V(x)-E ] y(x)\). Two cases are investigated:
(i) The potential \(V(x)\) is an even function with respect to \(x\). It is assumed, also, that \(y(x)\to 0\) for \(x\to\pm\infty\).
(ii) The general case for the Morse and Woods-Saxon potentials \(V(x)\).
The efficiency of the proposed methods is showed by comparing with the Runge-Kutta-Fehlberg 4(5) method.
(i) The potential \(V(x)\) is an even function with respect to \(x\). It is assumed, also, that \(y(x)\to 0\) for \(x\to\pm\infty\).
(ii) The general case for the Morse and Woods-Saxon potentials \(V(x)\).
The efficiency of the proposed methods is showed by comparing with the Runge-Kutta-Fehlberg 4(5) method.
Reviewer: S.Yanchuk (Kyïv)
MSC:
| 65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations |
| 34A34 | Nonlinear ordinary differential equations and systems |
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
| 34L40 | Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) |
