VODE: A variable-coefficient ODE solver. (English) Zbl 0677.65075

Brown, Peter N.; Byrne, George D.; Hindmarsh, Alan C.

SIAM J. Sci. Stat. Comput. 10, No. 5, 1038-1051 (1989).

This paper is concerned with the development of a new software package VODE for the numerical solution of (stiff and non-stiff) systems of ordinary differential equations. The new package can be considered as an up to day version of the well known EPISODE by the second and the third author [ACM Trans. Math. Software 1, 71-96 (1975; Zbl 0311.65049)]. Among the improvements that have been introduced we may mention a flexible user interface which is very similar to that of the ODEPACK solver LSODE. Also new algorithms for initial stepsize and stepsize and order change are used. Moreover, in the stiff case, the code has the possibility to save the Jacobian matrix to be used in the solution of the implicit equations by quasi Newton methods.
In this paper the authors consider also the fixed leading instead of the full variable coefficient version of the backward differentiation formula methods for stiff systems. They find that the first ones performs better on some problems, but the authors say that further testing is needed to have a clear understanding of their performance. The paper ends with some comparison tests with EPISODE using one and two-dimensional versions of a diurnal kinetics-transport problem. The dimensions are between 50 and 400 and the Jacobian is banded in all cases. It is found that the run time is reduced by an amount between 40 and 60 percent.

Reviewer: M.Calvo

MSC:

65L05	Numerical methods for initial value problems involving ordinary differential equations
65L50	Mesh generation, refinement, and adaptive methods for ordinary differential equations
65Yxx	Computer aspects of numerical algorithms
34-04	Software, source code, etc. for problems pertaining to ordinary differential equations
34A34	Nonlinear ordinary differential equations and systems

Keywords:

step size control; software package VODE; EPISODE; LSODE; algorithms; order change; quasi Newton methods; variable coefficient; backward differentiation formula methods; stiff systems; comparison tests

Citations:

Zbl 0311.65049

Software:

VODE