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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