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A New Methodology For The Construction Of Optimized Runge–Kutta–Nyström Methods

Author

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  • D. F. PAPADOPOULOS

    (Department of Business Administration, Faculty of Management and Economy, Educational Technological Institute of Patras, GR-26 334 Patras, Greece)

  • T. E. SIMOS

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

Abstract

In this paper, a new Runge–Kutta–Nyström method of fourth algebraic order is developed. The new method has zero phase-lag, zero amplification error and zero first integrals of the previous properties. Numerical results indicate that the new method is very efficient for solving numerically the Schrödinger equation. We note that for the first time in the literature we use the requirement of vanishing the first integrals of phase-lag and amplification error in the construction of efficient methods for the numerical solution of the Schrödinger equation.

Suggested Citation

  • D. F. Papadopoulos & T. E. Simos, 2011. "A New Methodology For The Construction Of Optimized Runge–Kutta–Nyström Methods," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 22(06), pages 623-634.
    • Handle: RePEc:wsi:ijmpcx:v:22:y:2011:i:06:n:s012918311101649x
    DOI: 10.1142/S012918311101649X
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