Description and use of LSODE, the Livemore Solver for Ordinary Differential Equations

Abstract

This document provides a comprehensive description of LSODE, a solver for initial value problems in ordinary differential equation systems. It is intended to bring together numerous materials documenting various aspects of LSODE, including technical reports on the methods used, published papers on LSODE, usage documentation contained within the LSODE source, and unpublished notes on algorithmic details. The three central chapters-n methods, code description, and code usage-are largely independent. Thus, for example, we intend that readers who are familiar with the solution methods and interested in how they are implemented in LSODE can read the Introduction and then chapter 3, Description of Code, without reading chapter 2, Description and Implementation of Methods. Similarly, those interested solely in how to use the code need read only the Introduction and then chapter 4, Description of Code Usage. In this case chapter 5, Example Problem, which illustrates code usage by means of a simple, stiff chemical kinetics problem, supplements chapter 4 and may be of further assistance. Although this document is intended mainly for users of LSODE, it can be used as supplementary reading material for graduate and advanced undergraduate courses on numerical methods. Engineers and scientists who use numerical solution methods for ordinary differential equations may also benefit from this document.