Abstract
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.
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Friesner, R.A., Tuckerman, L.S., Dornblaser, B.C. et al. A method for exponential propagation of large systems of stiff nonlinear differential equations. J Sci Comput 4, 327–354 (1989). https://doi.org/10.1007/BF01060992
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DOI: https://doi.org/10.1007/BF01060992