A method for exponential propagation of large systems of stiff nonlinear differential equations

A new time integrator for large, stiff systems of linear and nonlinear coupled differential equations is described. For linear systems, the method consists of forming a small (5-15-term) Krylov space using the Jacobian of the system and carrying out exact exponential propagation within this space. N...

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Bibliographic Details
Published in:Journal of scientific computing 1989-12, Vol.4 (4), p.327-354
Main Authors: Friesner, Richard A., Tuckerman, Laurette S., Dornblaser, Bright C., Russo, Thomas V.
Format: Article
Language:English
Subjects:
Numerical Analysis
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Summary:A new time integrator for large, stiff systems of linear and nonlinear coupled differential equations is described. For linear systems, the method consists of forming a small (5-15-term) Krylov space using the Jacobian of the system and carrying out exact exponential propagation within this space. Nonlinear corrections are incorporated via a convolution integral formalism; the integral is evaluated via approximate Krylov methods as well. Gains in efficiency ranging from factors of 2 to 30 are demonstrated for several test problems as compared to a forward Euler scheme and to the integration package LSODE.
ISSN:0885-7474
1573-7691
DOI:10.1007/BF01060992