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Exponentially Fitted Runge–Kutta Fourth Algebraic Order Methods For The Numerical Solution Of The Schrödinger Equation And Related Problems

Author

Listed:
  • 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)

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.

Suggested Citation

  • P. S. Williams & T. E. Simos, 2000. "Exponentially Fitted Runge–Kutta Fourth Algebraic Order Methods For The Numerical Solution Of The Schrödinger Equation And Related Problems," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 11(04), pages 785-807.
    • Handle: RePEc:wsi:ijmpcx:v:11:y:2000:i:04:n:s0129183100000687
    DOI: 10.1142/S0129183100000687
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