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

Abstract

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.

References in corpus (4)

• Error analysis of randomized Runge-Kutta methods for differential equations with time-irregular coefficients
• Randomized derivative-free Milstein algorithm for efficient approximation of solutions of SDEs under noisy information
• Optimal approximation of stochastic integrals in analytic noise model
• Efficient finite-dimensional solution of initial value problems in infinite-dimensional Banach spaces

Cited by in corpus (4)

• Existence, uniqueness and approximation of solutions to Carathéodory delay differential equations
• Convergence and stability of randomized implicit two-stage Runge-Kutta schemes
• Randomized Runge-Kutta-Nyström Methods for Unadjusted Hamiltonian and Kinetic Langevin Monte Carlo
• Euler scheme for approximation of solution of nonlinear ODEs under inexact information