On Runge-Kutta methods for parabolic problems with time-dependent coefficients

Author:
Ohannes A. Karakashian

Journal:
Math. Comp. **47** (1986), 77-101

MSC:
Primary 65N10; Secondary 65W05

DOI:
https://doi.org/10.1090/S0025-5718-1986-0842124-1

MathSciNet review:
842124

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Abstract: Galerkin fully discrete approximations for parabolic equations with time-dependent coefficients are analyzed. The schemes are based on implicit Runge-Kutta methods, and are coupled with preconditioned iterative methods to approximately solve the resulting systems of linear equations. It is shown that for certain classes of Runge-Kutta methods, the fully discrete equations exhibit parallel features that can be exploited to reduce the final execution time to that of a low-order method.

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DOI:
https://doi.org/10.1090/S0025-5718-1986-0842124-1

Article copyright:
© Copyright 1986
American Mathematical Society