An accurate eight order exponentially-fitted method for the efficient solution of the Schrodinger equation. T.E. Simos.

Title of program: MAPLESIM
Catalogue identifier: ADLI
Ref. in CPC: 125(2000)21
Distribution format: gzip file
Operating system: DOS, Windows
High speed store required: 20MK words
Number of bits in a word: 16
Number of lines in distributed program, including test data, etc: 641
Programming language used: Maple
Computer: IBM Compatible Pentium

Nature of physical 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).

Method of solution
Symbolic computation using Maple.

Typical running time
1800 seconds


 [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.