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Very High-Order A-stable Stiffly Accurate Diagonally Implicit Runge-Kutta Methods with Error Estimators

A numerical search approach is used to design high-order diagonally implicit Runge-Kutta (DIRK) schemes equipped with embedded error estimators, some of which have identical diagonal elements (SDIRK) and explicit first stage (ESDIRK). In each of these classes, we present new A-stable schemes of orders six (the highest order of previously known A-stable DIRK-type schemes) up to order eight. For each order, we include one scheme that is only A-stable as well as one that is stiffly accurate and/or L-stable. The latter require more stages but give better results for highly stiff problems and differential-algebraic equations (DAEs). The development of the eighth-order schemes requires, in addition to imposing A-stability, finding highly accurate numerical solutions for a system of 200 equations in over 100 variables, which is accomplished via a combination of global and local optimization strategies. The accuracy, stability, and efficiency of the schemes are demonstrated on diverse problems.

Identiferoai:union.ndltd.org:kaust.edu.sa/oai:repository.kaust.edu.sa:10754/693742
Date24 July 2023
CreatorsAlamri, Yousef
ContributorsKetcheson, David I., Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division, Bagci, Hakan, Parsani, Matteo
Source SetsKing Abdullah University of Science and Technology
LanguageEnglish
Detected LanguageEnglish
TypeThesis
Relationhttps://github.com/yousefalamri55/High_Order_DIRK_Methods_Coeffs

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