AN EMBEDDED 5(4) PAIR OF MODIFIED EXPLICIT RUNGE–KUTTA METHODS FOR THE NUMERICAL SOLUTION OF THE SCHRÖDINGER EQUATION-Reference-Cited by-同舟云学术

AN EMBEDDED 5(4) PAIR OF MODIFIED EXPLICIT RUNGE–KUTTA METHODS FOR THE NUMERICAL SOLUTION OF THE SCHRÖDINGER EQUATION

Published:2005-06 Issue:06 Volume:16 Page:879-894
ISSN:0129-1831
Container-title:International Journal of Modern Physics C
language:en
Short-container-title:Int. J. Mod. Phys. C

Author:

VAN DE VYVER HANS¹

Affiliation:

1. Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200 B, B-3001 Heverlee, Belgium

Abstract

A new way for constructing efficient embedded modified Runge–Kutta methods for the numerical solution of the Schrödinger equation is presented in this paper. The methods of the embedded scheme have algebraic orders five and four. Applications of the new pair to the elastic scattering phase-shift problem and coupled differential equations of Schrödinger type indicate that the new pair is much more efficient than other well known comparable embedded Runge–Kutta pairs.

Publisher

World Scientific Pub Co Pte Lt

Subject

Computational Theory and Mathematics,Computer Science Applications,General Physics and Astronomy,Mathematical Physics,Statistical and Nonlinear Physics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0129183105007625

Reference31 articles.

1. T. E. Simos, Chemical Modeling–Applications and Theory, Vol. 1, Specialist Periodical Reports (The Royal Society of Chemistry, Cambridge, 2000) pp. 38–142.

2. T. E. Simos, Chemical Modeling–Applications and Theory, Vol. 2, Specialist Periodical Reports (The Royal Society of Chemistry, Cambridge, 2002) pp. 170–270.

3. T. E. Simos, Chemical Modeling–Applications and Theory, Vol. 3, Specialist Periodical Reports (The Royal Society of Chemistry, Cambridge, 2004) pp. 271–378.

4. Two-step fourth orderP-stable methods for second order differential equations

5. A Noumerov-type method with minimal phase-lag for the integration of second order periodic initial-value problems

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