This repository accompanies the manuscript "VERY HIGH-ORDER A-STABLE STIFFLY ACCURATE DIAGONALLY IMPLICIT RUNGE-KUTTA METHODS WITH ERROR ESTIMATORS" available here https://arxiv.org/abs/2211.14574
It contains the coefficients for a 6th, 7th, and 8th order DIRK-type methods and their embedded error estimators. The notation used is
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TYPE: is the structure of the DIRK-type method, that is DIRK, EDIRK, SDIRK, or ESDIRK.
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$s$ : number of stages for the advancing method. -
$p$ : order of convergence for the advancing method. -
$r$ : stage order of the advancing method. -
$X$ : stability property of the advancing method; i.e.,$A$ for A-stable,$L$ for L-stable,$SA$ for stiffly accurate, or$SAL$ if both stiffly accurate and L-stable. -
$\widehat{s}$ : number of stages for the embedded error estimator. -
$\widehat{p}$ : order of convergence for the embedded error estimator. -
$Y$ : stability property of the embedded error estimator, if any.
Note that in some methods
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Sixth-order methods
$\texttt{DIRK(6,6)[1]A-[(7,5)A]}$ $\texttt{DIRK(8,6)[1]SAL-[(8,5)A]}$ $\texttt{ESDIRK(8,6)[2]SA-[(8,4)]}$ $\texttt{SDIRK(9,6)[1]SAL-[(9,5)A]}$
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Seventh-order methods
$\texttt{DIRK(9,7)[1]A-[(9,5)A]}$ $\texttt{DIRK(10,7)[1]SAL-[(10,5)A]}$ $\texttt{ESDIRK(10,7)[2]SA-[(10,5)]}$ $\texttt{SDIRK(11,7)[1]SAL-[(11,5)A]}$
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Eighth-order methods
$\texttt{DIRK(13,8)[1]A-[(14,6)A]}$ $\texttt{DIRK(15,8)[1]SAL-[(16,6)A]}$ $\texttt{ESDIRK(16,8)[2]SAL-[(16,5)]}$