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

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 tha...

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Bibliographic Details
Published in:Mathematics of computation 1986, Vol.47 (175), p.77-101
Main Author: Karakashian, Ohannes A.
Format: Article
Language:English
Subjects:
Approximation
Coefficients
Eigenvalues
Estimation methods
Exact sciences and technology
Integers
Iterative methods
Linear systems
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Partial differential equations, miscellaneous problems
Rational functions
Research article
Runge Kutta method
Sciences and techniques of general use
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Summary: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.
ISSN:0025-5718
1088-6842
DOI:10.1090/S0025-5718-1986-0842124-1