PROGRAM SUMMARY
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
Keywords:
Computer algebra, Maple programming, Construction of
exponentially-fitted methods.
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
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.