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A New Symmetric Eight-Step Predictor-Corrector Method For The Numerical Solution Of The Radial Schrödinger Equation And Related Orbital Problems

Author

Listed:
  • G. A. PANOPOULOS

    (Laboratory of Computational Sciences, Department of Computer Science and Technology, Faculty of Sciences and Technology, University of Peloponnese, GR-22 100 Tripolis, Greece)

  • Z. A. ANASTASSI

    (Department of Sciences, School of Pedagogical, and Technological Education (ASPETE), N. Heraklion GR-14121 Athens, Greece)

  • T. E. SIMOS

    (Laboratory of Computational Sciences, Department of Computer Science and Technology, Faculty of Sciences and Technology, University of Peloponnese, GR-22 100 Tripolis, Greece;
    Department of Mathematics, College of Sciences, King Saud University, P. O. Box 2455, Riyadh 11451, Saudi Arabia)

Abstract

A new general multistep predictor-corrector (PC) pair form is introduced for the numerical integration of second-order initial-value problems. Using this form, a new symmetric eight-step predictor-corrector method with minimal phase-lag and algebraic order ten is also constructed. The new method is based on the multistep symmetric method of Quinlan–Tremaine,1with eight steps and 8th algebraic order and is constructed to solve numerically the radial time-independent Schrödinger equation. It can also be used to integrate related IVPs with oscillating solutions such as orbital problems. We compare the new method to some recently constructed optimized methods from the literature. We measure the efficiency of the methods and conclude that the new method with minimal phase-lag is the most efficient of all the compared methods and for all the problems solved.

Suggested Citation

  • G. A. Panopoulos & Z. A. Anastassi & T. E. Simos, 2011. "A New Symmetric Eight-Step Predictor-Corrector Method For The Numerical Solution Of The Radial Schrödinger Equation And Related Orbital Problems," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 22(02), pages 133-153.
    • Handle: RePEc:wsi:ijmpcx:v:22:y:2011:i:02:n:s0129183111016154
    DOI: 10.1142/S0129183111016154
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