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arXiv · 2404.19059

Convergence and stability of randomized implicit two-stage Runge-Kutta schemes

Tomasz Bochacik·Paweł Przybyłowicz
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Abstract

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.

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Tomasz Bochacik, Paweł Przybyłowicz. 2024-04-29. Convergence and stability of randomized implicit two-stage Runge-Kutta schemes. https://doi.org/10.1007/s10543-024-01050-9

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