A NEW METHODOLOGY FOR THE CONSTRUCTION OF OPTIMIZED RUNGE–KUTTA–NYSTRÖM METHODS

D. F. Papadopoulos and T. E. Simos ()
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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;

International Journal of Modern Physics C (IJMPC), 2011, vol. 22, issue 06, 623-634

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.

Keywords: Runge–Kutta–Nyström methods; phase-fitted; amplification-fitted; integrals; Schrödinger; phase-lag infinity; 0.260; 95.10.E (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1142/S012918311101649X

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