EXPONENTIALLY FITTED RUNGE–KUTTA FOURTH ALGEBRAIC ORDER METHODS FOR THE NUMERICAL SOLUTION OF THE SCHRÖDINGER EQUATION AND RELATED PROBLEMS

P. S. Williams () and T. E. Simos ()
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P. S. Williams: Department of Computing, Information Systems and Mathematics, London Guildhall University, 100 Minories, London EC3N 1JY, UK
T. E. Simos: Department of Civil Engineering, School of Engineering, Democritus University of Thrace GR-671 00 Xanthi, Greece

International Journal of Modern Physics C (IJMPC), 2000, vol. 11, issue 04, 785-807

Abstract: Fourth order exponential and trigonometric fitted Runge–Kutta methods are developed in this paper. They are applied to problems involving the Schrödinger equation and to other related problems. Numerical results show the superiority of these methods over conventional fourth order Runge–Kutta methods. Based on the methods developed in this paper, a variable-step algorithm is proposed. Numerical experiments show the efficiency of the new algorithm.

Keywords: Runge–Kutta Methods; Schrödinger Equation; Eigenvalue Problems; Explicit Methods; Exponential Fitting (search for similar items in EconPapers)
Date: 2000
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DOI: 10.1142/S0129183100000687

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