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

Hans van de Vyver
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Hans van de Vyver: Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200 B, B-3001 Heverlee, Belgium

International Journal of Modern Physics C (IJMPC), 2005, vol. 16, issue 06, 879-894

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.

Keywords: Explicit Runge–Kutta methods; embedded Runge–Kutta methods; variable stepsize algorithms; phase-shift problem; coupled differential equations of Schrödinger type (search for similar items in EconPapers)
Date: 2005
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DOI: 10.1142/S0129183105007625

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