Differential/Algebraic Equations are not ODE’<scp>s</scp>

Abstract

This paper outlines a number of difficulties which can arise when numerical methods are used to solve systems of differential/algebraic equations of the form ${\bf F}(t,{\bf y},{\bf y}') = {\bf 0}$. Problems which can be written in this general form include standard ODE systems as well as problems which are substantially different from standard ODE’S. Some of the differential/algebraic systems can be solved using numerical methods which are commonly used for solving stiff systems of ordinary differential equations. Other problems can be solved using codes based on the stiff methods, but only after extensive modifications to the error estimates and other strategies in the code. A further class of problems cannot be solved at all with such codes, because changing the stepsize causes large errors in the solution. We describe in detail the causes of these difficulties and indicate solutions in some cases.