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

Karakashian, Ohannes A.

doi:10.1090/S0025-5718-1986-0842124-1

On Runge-Kutta methods for parabolic problems with time-dependent coefficients
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by Ohannes A. Karakashian PDF

Math. Comp. 47 (1986), 77-101 Request permission

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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Approximations for Parabolic Equations with Time-Dependent Coefficients

Convergence Estimates for Semidiscrete Parabolic Approximations

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