Euler scheme for approximation of solution of nonlinear ODEs under inexact information
arXiv:2209.07482 · doi:10.1016/j.apnum.2023.08.002
Abstract
We investigate error of the Euler scheme in the case when the right-hand side function of the underlying ODE satisfies nonstandard assumptions such as local one-sided Lipschitz condition and local Hölder continuity. Moreover, we assume two cases in regards to information availability: exact and noisy with respect to the right-hand side function. Optimality analysis of the Euler scheme is also provided. Finally, we present the results of some numerical experiments.
arXiv comment18 pages, 9 figures
References in corpus (6)
- On Wavelet-Galerkin methods for Semilinear Parabolic Equations with Additive Noise
- Randomized derivative-free Milstein algorithm for efficient approximation of solutions of SDEs under noisy information
- Randomized Runge-Kutta method -- stability and convergence under inexact information
- On mathematical aspects of evolution of dislocation density in metallic materials
- Optimal approximation of stochastic integrals in analytic noise model
- Efficient finite-dimensional solution of initial value problems in infinite-dimensional Banach spaces