Efficient Integration Methods for Stiff Systems of Ordinary Differential Equations

Abstract

Linear one step methods of a novel design are given for the numerical solution of stiff systems of ordinary differential equations. These methods permit fast integration with increments h of the independent variable adjusted to the slowly varying, dominant solutions. The integration formulas owe their efficiency to combining a reasonable order of accuracy for $h \to 0$ with a precise simulation of specific rapidly varying solutions, and with A-stability in the sense of Dahlquist.