Convergence and stability of randomized implicit two-stage Runge-Kutta schemes
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913652717649920 |
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| author | Bochacik, Tomasz Przybyłowicz, Paweł |
| author_facet | Bochacik, Tomasz Przybyłowicz, Paweł |
| contents | We randomize the implicit two-stage Runge-Kutta scheme in order to improve the rate of convergence (with respect to a deterministic scheme) and stability of the approximate solution (with respect to the solution generated by the explicit scheme). For stability analysis, we use Dahlquist's concept of A-stability, adopted to randomized schemes by considering three notions of stability: asymptotic, mean-square, and in probability. The randomized implicit RK2 scheme proves to be A-stable asymptotically and in probability but not in the mean-square sense. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_19059 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convergence and stability of randomized implicit two-stage Runge-Kutta schemes Bochacik, Tomasz Przybyłowicz, Paweł Numerical Analysis 65C05, 65C20, 65L05, 65L06, 65L70 We randomize the implicit two-stage Runge-Kutta scheme in order to improve the rate of convergence (with respect to a deterministic scheme) and stability of the approximate solution (with respect to the solution generated by the explicit scheme). For stability analysis, we use Dahlquist's concept of A-stability, adopted to randomized schemes by considering three notions of stability: asymptotic, mean-square, and in probability. The randomized implicit RK2 scheme proves to be A-stable asymptotically and in probability but not in the mean-square sense. |
| title | Convergence and stability of randomized implicit two-stage Runge-Kutta schemes |
| topic | Numerical Analysis 65C05, 65C20, 65L05, 65L06, 65L70 |
| url | https://arxiv.org/abs/2404.19059 |