Large ordinary differential equation systems and software

Abstract

Over the last decade, the need to solve large stiff and nonstiff ordinary differential equation systems (initial value problems) has led to considerable software, mostly based on the methods of Adams (nonstiff case) and Gear (stiff case). The growing number of good general purpose initial value solvers has fueled discussions on the idea of a systematized collection of such solvers, called ODE-PACK. In recent years, a tentative user interface standard was developed, and an initial collection of five solvers was written, primarily at LLNL. These solvers handle stiff and nonstiff problems posed in standard (explicit) form, problems in linearly implicit form, full Jacobians, banded Jacobians, general sparse Jacobians, and problems with rootfinding requirements. They include solvers with automatic (stiff/nonstiff) method selection. These solvers are described briefly here, and their capabilities are illustrated with an example problem arising from a system of PDE's modeling atmospheric kinetics-transport.