EXPLICIT NUMEROV TYPE METHODS FOR SECOND ORDER IVPsWITH OSCILLATING SOLUTIONS

G. Papageorgiou (), Ch. Tsitouras () and I. Th. Famelis ()
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G. Papageorgiou: Department of Applied Mathematics and Physical Sciences, National Technical University of Athens, Zografou Campus 15780, Athens, Greece
Ch. Tsitouras: Department of Applied Mathematics and Physical Sciences, National Technical University of Athens, Zografou Campus 15780, Athens, Greece
I. Th. Famelis: Department of Applied Mathematics and Physical Sciences, National Technical University of Athens, Zografou Campus 15780, Athens, Greece

International Journal of Modern Physics C (IJMPC), 2001, vol. 12, issue 05, 657-666

Abstract: New explicit hybrid Numerov type methods are presented in this paper. These efficient methods are constructed using a new approach, where we do not need the use of the intermediate high accuracy interpolatory nodes, since only the Taylor expansion of the internal points is needed. The methods share sixth algebraic order at a cost of five stages per step while their phase-lag order is 14 and partly satisfy the dissipation order conditions. It has be seen that the property of phase-lag is more important than the nonempty interval in constructing numerical methods for the solution of Schrödinger equation and related problems.1–3Numerical results over some well known problems in physics and mechanics indicate the superiority of the new methods.

Keywords: Initial Value Problems (IVP); Numerical Solution; Hybrid Numerov Methods; Phase-Lag; 04.20.E; 02.60 (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1142/S0129183101001869

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