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Manuscript Title: An accurate eight order exponentially-fitted method for the efficient solution of the Schrodinger equation.
Authors: T.E. Simos
Program title: MAPLESIM
Catalogue identifier: ADLI_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 125(2000)21
Programming language: Maple.
Computer: IBM Compatible Pentium.
Operating system: DOS, Windows.
RAM: 20M words
Word size: 16
Keywords: Computer algebra, Maple programming, Construction of Exponentially-fitted Methods.
Classification: 5.

Nature of problem:
With the present program the derivation of the coefficients produced by the equation (14) is obtained. The first part of the proposed program consists of the calculation of the matrix elements which form the coefficients of the system of equations. The second part of the proposed program, as this has been explained in [1], [2] and [3], consists of the iterative application of the L'Hospital's rule (to avoid coefficients of the form 0/0) for the computation of the solution of these equations that make up the coefficients of the method (14). We note that the system of equations produced by the equation (14) is solved by an application of Cramer's rule. The above procedure is repeated for the calculation of the coefficients of the methods (24)-(25) and for the methods (28)-(29).

Solution method:
Symbolic computation using Maple.

Running time:
1800 seconds

References:
[1] T. Lyche, Chebyshevian multistep methods for ordinary differential equations, Numerische Mathematik, 10 (1972) 65-75.
[2] A.D. Raptis, Exponential multistep methods for ordinary differential equations, Bulletin of the Greek Mathematical Society, 25 (1984) 113-126.
[3] T.E. Simos, Numerical solution of ordinary differential equations with periodical solution. Doctoral Dissertation, National Technical University of Athens, 1990.