A Comparison of ODE Solution Methods for Spacecraft Thermal Problems

摘要

In spacecraft thermal design and analysis practice, the lumped-parameter network formulation is used extensively to construct mathematical models. The models take the form of a system of coupled, nonlinear, first-order ordinary differential equations (ODEs). The number of equations may vary from a few tens to a few thousands. It is necessary to solve these equations in an efficient and economical way. This article reviews various methods available for the numerical solution of ODEs. General-purpose codes available for this are discussed. Numerical experiments are conducted to investigate the efficiency of various methods. The results indicate that the Crank-Nicholson method with provision for automatic selection of step size to control the local truncation error is a very good choice for the solution of spacecraft thermal problems.