On Stability and Accuracy of Numerical Integration Methods for Stiff Differential Equations,
IBM THOMAS J WATSON RESEARCH CENTER YORKTOWN HEIGHTS N Y
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This paper surveys research concerning the stability and accuracy of numerical integration methods for stiff systems of ordinary differential equations. First, the theory of A-stability of linear multistep methods is reviewed. Second, weaker concepts of unconditional fixed-h stability are discussed. Third, examples of A-stable methods of high orders of accuracy are given. Fourth, results relating the order of accuracy to various stability concepts are listed. Fifth, some recent work concerning asymptotic stability of non-linear multistep difference equations is summarized.
- Numerical Mathematics