A new family of exponentially fitted methods

Authors:
P. S. Williams;T. E. Simos
Affiliations:
Department of Computing, Information Systems and Mathematics London Guildhall University 100 Minories, London EC3N 1JY, U.K.;Department of Computer Science and Technology, Faculty of Sciences and Technology University of Peloponnese GR-221 00 Tripolis, Greece
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2003

Citing 7
Cited 1

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A family of Numerov-type exponentially fitted predictor-corrector methods for the numerical integration of the radial Schro¨dinger equation

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A smart nonstandard finite difference scheme for second order nonlinear boundary value problems

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Abstract

An exponentially-fitted method is developed in this paper. This is a higher-order extension of the dissipative (i.e., nonsymmetric) two-step method first described by Simos and Williams in [1], for the numerical integration of the Schrodinger equation. An application to the bound-states problem and the resonance problem of the radial Schrodinger equation indicates that the new method is more efficient than the classical dissipative method and other well-known methods. Based on the new method and the method of Raptis and Allison [2] a new variable-step method is obtained. The application of the new variable-step method to some coupled differential equations arising from the Schrodinger equation indicates the efficiency of the new approach.