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Stiff systems of ordinary differential equations. Part 1. Completely stiff, homogeneous systems

Published online by Cambridge University Press:  17 February 2009

J. J. Mahony  and
J. J. Shepherd
J. J. Mahony
Affiliation:
Department of Mathematics, University of Western Australia, Nedlands, Western Australia 6009
J. J. Shepherd
Affiliation:
Department of Mathematics, University of Western Australia, Nedlands, Western Australia 6009
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Abstract

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For the completely stiff real homogeneous system

where e is a small positive parameter, a method is given for the construction of a basis for the solution space.

If A has n linearly independent eigenvector functions, then there exists a choice of these, {si}, with corresponding eigenvalue functions {λi}, such that there is a local basis for solution, that takes the form

where vi is a vector that tends to zero with e. In general, a basis of this form exists only on an interval in which the distinct eigenvalues have their real parts ordered. A construction is provided for continuing any solution across the boundaries of any such interval. These results are proved for a finite or infinite interval for which there are only a finite number of points at which the ordering of the real parts of eigenvalues changes.

Type
Research Article
Information
The ANZIAM Journal , Volume 23 , Issue 1 , July 1981 , pp. 17 - 51
Copyright
Copyright © Australian Mathematical Society 1981

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