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A New Explicit Four-Step Symmetric Method for Solving Schrödinger’s Equation

Author

Listed:
  • Saleem Obaidat

    (Mathematics Department, College of Science, King Saud University, Riyadh 11451, Saudi Arabia
    Current address: Mathematics Department, College of Science, P.O.Box 2455, Riyadh 11451, Saudi Arabia.
    These authors contributed equally to this work.)

  • Said Mesloub

    (Mathematics Department, College of Science, King Saud University, Riyadh 11451, Saudi Arabia
    Current address: Mathematics Department, College of Science, P.O.Box 2455, Riyadh 11451, Saudi Arabia.
    These authors contributed equally to this work.)

Abstract

In this article we have developed a new explicit four-step linear method of fourth algebraic order with vanished phase-lag and its first derivative. The efficiency of the method is tested by solving effectively the one-dimensional time independent Schrödinger’s equation. The error and stability analysis are studied. Also, the new method is compared with other methods in the literature. It is found that this method is more efficient than these methods.

Suggested Citation

  • Saleem Obaidat & Said Mesloub, 2019. "A New Explicit Four-Step Symmetric Method for Solving Schrödinger’s Equation," Mathematics, MDPI, vol. 7(11), pages 1-12, November.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:11:p:1124-:d:287851
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    References listed on IDEAS

    as
    1. Junyan Ma & T. E. Simos, 2016. "Hybrid high algebraic order two-step method with vanished phase-lag and its first, second, third, fourth and fifth derivatives," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 27(05), pages 1-20, May.
    2. T. E. Simos & Jesus Vigo Aguiar, 2001. "A Symmetric High Order Method With Minimal Phase-Lag For The Numerical Solution Of The Schrödinger Equation," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 12(07), pages 1035-1042.
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