SOLVING STIFF DIFFERENTIAL-EQUATIONS WITH THE METHOD OF PATCHES

We introduce a new method for solving very stiff sets of ordinary diff erential equations. The basic idea is to replace the original nanlinea r equations with a set of equally stiff equations that are piecewise L inear, and therefore can be solved exactly. We demonstrate the value o f the method on small systems of equations for which some other method s are inefficient or produce spurious solutions, estimate error bounds , and discuss extensions of the method to larger systems of equations and to partial differential equations. (C) 1998 Academic Press.