EXPFIT4 – a FORTRAN program for the numerical solution of systems of nonlinear second-order initial-value problems. (English) Zbl 0927.65099

Ixaru, L. Gr.; De Meyer, H.; Vanden Berghe, G.; Van Daele, M.

Comput. Phys. Commun. 100, No. 1-2, 71-80 (1997).

Summary: We present a FORTRAN program which solves the initial-value problem associated with nonstiff systems of the form \(y''= f(x,y)\). The program is based on a family of exponential-fitted four-step methods. The presented code is particularly suited to solve second-order initial-value problems arising from physics.

MSC:

65L06	Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
34-04	Software, source code, etc. for problems pertaining to ordinary differential equations
65L05	Numerical methods for initial value problems involving ordinary differential equations
34A34	Nonlinear ordinary differential equations and systems
65L50	Mesh generation, refinement, and adaptive methods for ordinary differential equations

Keywords:

Newtonian physics; celestial mechanics; linear and nonlinear second-order differential equations; initial-value problems; exponential fitting; multistep methods; stepsize control

Software:

EXPFIT4

References:

[1]	Ixaru, L. Gr.; Berghe, G. Vanden; De Meyer, H.; Van Daele, M., Comput. Phys. Commun., 100, 56 (1997)
[2]	Ixaru, L. Gr.; De Meyer, H.; Berghe, G. Vanden; Van Daele, M., Numer. Lin. Alg. Appl., 3, 81 (1996)
[3]	Hairer, E.; Nørsett, S. P.; Wanner, G., Solving Ordinary Differental Equations I. Nonstiff Problems (1987), Springer: Springer Berlin · Zbl 0638.65058
[4]	Ixaru, L. Gr., Numerical Methods for Differential Equations (1984), Reidel: Reidel Dordrecht · Zbl 0301.34010
[5]	Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; Vetterling, W. T., Numerical Recipes — the Art of Scientific Computing FORTRAN (1986), Cambridge Univ. Press: Cambridge Univ. Press Cambridge · Zbl 0587.65003
[6]	Parallel Fortran (version 2.1.3). Parallel Fortran (version 2.1.3), User Guide, 3L Ltd. (1990), UK