A NEW MODIFIED RUNGE–KUTTA–NYSTRÖM METHOD WITH PHASE-LAG OF ORDER INFINITY FOR THE NUMERICAL SOLUTION OF THE SCHRÖDINGER EQUATION AND RELATED PROBLEMS

T. E. Simos () and Jesus Vigo Aguiar
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T. E. Simos: Section of Mathematics, Department of Civil Engineering, School of Engineering, Democritus University of Thrace, GR-671 00 Xanthi, Greece
Jesus Vigo Aguiar: Departamento de Matematica Aplicada, Facultad de Ciencias, Universidad de Salamanca, 37008 Salamanca, Spain

International Journal of Modern Physics C (IJMPC), 2000, vol. 11, issue 06, 1195-1208

Abstract: In this paper, a new approach for developing efficient Runge–Kutta–Nyström methods is introduced. This new approach is based on the requirement of annihilation of the phase-lag (i.e., the phase-lag is of order infinity) and on a modification of Runge–Kutta–Nyström methods. Based on this approach, a new modified Runge–Kutta–Nyström fourth algebraic order method is developed for the numerical solution of Schrödinger equation and related problems. The new method has phase-lag of order infinity and extended interval of periodicity. Numerical illustrations on the radial Schrödinger equation and related problems with oscillating solutions indicate that the new method is more efficient than older ones.

Keywords: Runge–Kutta–Nyström Methods; Radial Schrödinger Equation; Resonance Problems; Scattering Problems; Phase Shift Problems; Phase-Lag; Phase-Fitted; Oscillating Solutions (search for similar items in EconPapers)
Date: 2000
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DOI: 10.1142/S0129183100001036

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