Practical improvements to SIMPR codes for stiff ODEs
type: Item
instance of: scholarly article
title: Practical improvements to SIMPR codes for stiff ODEs
zbMATH Open document ID: 0678.65048
DOI: 10.1016/0096-3003(89)90126-4
published in: Applied Mathematics and Computation
publication date: 1989-01-01T00:00:00Z
review text: The paper discusses codes using extrapolation of the semi-implicit mid- point rule for the solution of stiff ordinary differential equations (ODEs). Some comparisons are made between applying such a code to systems of equations in autonomous form or non-autonomous form. Arguments in favour of using the autonomous form are given and numerical evidence is also presented that prior conversion of the ODEs to autonomous form may produce significantly better results. A way of writing the code so that this conversion is not required of the user is derived. It is argued that methods of extrapolation type can have problems with a stepsize which is out of scale. A stability monitor is derived for the purpose of rejecting such a step as early as possible in the interests of efficiency and of avoiding more serious difficulties. Some tests using the new monitor are described.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L50
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 4111925
zbMATH Keywords: stiff systems
zbMATH Keywords: scaled stepsizes
zbMATH Keywords: extrapolation
zbMATH Keywords: semi-implicit mid-point rule
zbMATH Keywords: comparisons
zbMATH Keywords: autonomous form
zbMATH Keywords: stability
author: L. F. Shampine
MaRDI profile type: Publication
full work available at URL: 0096-3003(89)90126-4
OpenAlex ID: W4237976969
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description: scientific article; zbMATH DE number 4111925