On the stability and accuracy of onestep methods for solving stiff systems of ordinary differential equations
Authors:
A. Prothero and A. Robinson
Journal:
Math. Comp. 28 (1974), 145162
MSC:
Primary 65L05
MathSciNet review:
0331793
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Abstract: The stiffness in some systems of nonlinear differential equations is shown to be characterized by single stiff equations of the form The stability and accuracy of numerical approximations to the solution , obtained using implicit onestep integration methods, are studied. An Sstability property is introduced for this problem, generalizing the concept of Astability. A set of stiffly accurate onestep methods is identified and the concept of stiff order is defined in the limit . These additional properties are enumerated for several classes of Astable onestep methods, and are used to predict the behaviour of numerical solutions to stiff nonlinear initialvalue 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:
http://dx.doi.org/10.1090/S00255718197403317932
PII:
S 00255718(1974)03317932
Keywords:
Stiff system of ordinary differential equations,
implicit onestep methods,
Astability,
Sstability,
stiffly accurate methods,
stiff order
Article copyright:
© Copyright 1974 American Mathematical Society
