DeepAI

# Randomized Runge-Kutta method – stability and convergence under inexact information

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 randomized two-stage Runge-Kutta scheme is the optimal method among all randomized algorithms based on standard noisy information. We perform numerical experiments that confirm our theoretical findings. Moreover, for the optimal algorithm we rigorously investigate properties of regions of absolute stability.

• 4 publications
• 1 publication
• 4 publications
• 15 publications
05/22/2022

### A note on the probabilistic stability of randomized Taylor schemes

We study the stability of randomized Taylor schemes for ODEs. We conside...
04/30/2021

### On the randomized Euler schemes for ODEs under inexact information

We analyse errors of randomized explicit and implicit Euler schemes for ...
05/09/2016

### Randomized Kaczmarz for Rank Aggregation from Pairwise Comparisons

We revisit the problem of inferring the overall ranking among entities i...
12/14/2019

### Randomized derivative-free Milstein algorithm for efficient approximation of solutions of SDEs under noisy information

We deal with pointwise approximation of solutions of scalar stochastic d...
02/03/2022

### On the properties of the exceptional set for the randomized Euler and Runge-Kutta schemes

We show that the probability of the exceptional set decays exponentially...
12/01/2022

### Randomized Milstein algorithm for approximation of solutions of jump-diffusion SDEs

We investigate the error of the randomized Milstein algorithm for solvin...
01/11/2021

### On the power of standard information for tractability for L_2-approximation in the randomized setting

We study approximation of multivariate functions from a separable Hilber...