10 citations · 12 across the 4 of their papers we have counts for
4 papers
Convergence and stability of randomized implicit two-stage Runge-Kutta schemes
Tomasz Bochacik, Paweł Przybyłowicz
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 solutio…
On the properties of the exceptional set for the randomized Euler and Runge-Kutta schemes
Tomasz Bochacik
We show that the probability of the exceptional set decays exponentially for a broad class of randomized algorithms approximating solutions of ODEs, admitting a certain error decom…
On the randomized Euler schemes for ODEs under inexact information
Tomasz Bochacik, Paweł Przybyłowicz
We analyse errors of randomized explicit and implicit Euler schemes for approximate solving of ordinary differential equations (ODEs). We consider classes of ODEs for which the rig…
Randomized Runge-Kutta method -- stability and convergence under inexact information
Tomasz Bochacik, Maciej Goćwin, Paweł M. Morkisz +1
We deal with optimal approximation of solutions of ODEs under local Lipschitz condition and inexact discrete information about the right-hand side functions. We show that the rando…