On the stability and accuracy of one-step methods for solving stiff systems of ordinary differential equations

Authors:
A. Prothero and A. Robinson

Journal:
Math. Comp. **28** (1974), 145-162

MSC:
Primary 65L05

DOI:
https://doi.org/10.1090/S0025-5718-1974-0331793-2

MathSciNet review:
0331793

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Abstract | References | Similar Articles | Additional Information

Abstract: The stiffness in some systems of nonlinear differential equations is shown to be characterized by single stiff equations of the form

*S*-stability property is introduced for this problem, generalizing the concept of

*A*-stability. A set of stiffly accurate one-step methods is identified and the concept of stiff order is defined in the limit . These additional properties are enumerated for several classes of

*A*-stable one-step methods, and are used to predict the behaviour of numerical solutions to stiff nonlinear initial-value problems obtained using such methods. A family of methods based on a compromise between accuracy and stability considerations is recommended for use on practical problems.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1974-0331793-2

Keywords:
Stiff system of ordinary differential equations,
implicit one-step methods,
*A*-stability,
*S*-stability,
stiffly accurate methods,
stiff order

Article copyright:
© Copyright 1974
American Mathematical Society