An adaptive time-stepping method based on a posteriori weak error analysis for large SDE systems
type: Item
instance of: scholarly article
title: An adaptive time-stepping method based on a posteriori weak error analysis for large SDE systems
zbMATH Open document ID: 1491.65016
author: Fabian Merle
author: Andreas Prohl
published in: Numerische Mathematik
publication date: 2021-12-01T00:00:00Z
review text: In this paper, a numerical scheme based on the semi-implicit Euler method is constructed to approximate solutions of a class of systems of stochastic differential equations. An adaptive mesh strategy (using quasi deterministic rather than random meshes) is developed in which local step size is chosen using an a posteriori weak error estimator. The authors prove convergence with optimal weak order for the estimator and an algorithm for weak adaptive approximation is presented. Then they prove the number of iterations necessary to generate each local step size and the number of time steps needed to cover the desired finite interval. The paper concludes with results of numerical experiments that illustrate advantages of this adaptive strategy over a uniform step size strategy.
Mathematics Subject Classification ID: 65C30
Mathematics Subject Classification ID: 60H35
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 65Y20
zbMATH DE Number: 7437237
zbMATH Keywords: stochastic differential equations
zbMATH Keywords: adaptive time-stepping
zbMATH Keywords: weak error estimate
reviewed by: Melvin D. Lax
MaRDI profile type: Publication
full work available at URL: s00211-021-01233-4
OpenAlex ID: W3207472838
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DOI: 10.1007/S00211-021-01233-4
description: scientific article; zbMATH DE number 7437237