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.
| Identifer | oai:union.ndltd.org:kaust.edu.sa/oai:repository.kaust.edu.sa:10754/693742 |
| Date | 24 July 2023 |
| Creators | Alamri, Yousef |
| Contributors | Ketcheson, David I., Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division, Bagci, Hakan, Parsani, Matteo |
| Source Sets | King Abdullah University of Science and Technology |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Relation | https://github.com/yousefalamri55/High_Order_DIRK_Methods_Coeffs |
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