ATOMFT: Solving ODEs and DAEs using Taylor Series

Authors

Y. F. Chang
George F. Corliss, Marquette UniversityFollow

Document Type

Article

Language

eng

Publication Date

11-1994

Publisher

Elsevier

Source Publication

Computers & Mathematics with Applications

Source ISSN

0898-1221

Abstract

Taylor series methods compute a solution to an initial value problem in ordinary differential equations by expanding each component of the solution in a long Taylor series. The series terms are generated recursively using the techniques of automatic differentiation. The ATOMFT system includes a translator to transform statements of the system of ODEs into a FORTRAN 77 object program that is compiled, linked with the ATOMFT runtime library, and run to solve the problem. We review the use of the ATOMFT system for nonstiff and stiff ODEs, the propagation of global errors, and applications to differential algebraic equations arising from certain control problems, to boundary value problems, to numerical quadrature, and to delay problems.

Comments

Computers & Mathematics with Applications, Vol. 28, No. 10-12 (November-December 1994): 209-233. DOI.

Recommended Citation

Chang, Y. F. and Corliss, George F., "ATOMFT: Solving ODEs and DAEs using Taylor Series" (1994). Electrical and Computer Engineering Faculty Research and Publications. 311.
https://epublications.marquette.edu/electric_fac/311