An asymptotic preserving semi-implicit multiderivative solver
| Autor: | Jochen Schütz, David C. Seal |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Numerical Analysis
65L20 Applied Mathematics MathematicsofComputing_NUMERICALANALYSIS Ode Context (language use) Numerical Analysis (math.NA) 010103 numerical & computational mathematics Function (mathematics) Solver 01 natural sciences 010101 applied mathematics Computational Mathematics symbols.namesake Consistency (statistics) Ordinary differential equation ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION FOS: Mathematics Taylor series symbols Applied mathematics Limit (mathematics) Mathematics - Numerical Analysis 0101 mathematics Mathematics |
| Popis: | In this work we construct a multiderivative implicit-explicit (IMEX) scheme for a class of stiff ordinary differential equations. Our solver is high-order accurate and has an asymptotic preserving (AP) property. The proposed method is based upon a two-derivative backward Taylor series base solver, which we show has an AP property. Higher order accuracies are found by iterating the result over a high-order multiderivative interpolant of the right hand side function, which we again prove has an AP property. Theoretical results showcasing the asymptotic consistency as well as the high-order accuracy of the solver are presented. In addition, an extension of the solver to an arbitrarily split right hand side function is also offered. Numerical results for a collection of standard test cases from the literature are presented that support the theoretical findings of the paper. 18 Pages |
| Databáze: | OpenAIRE |
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