The composite Euler method for stiff stochastic differential equations

Kevin Burrage, Tianhai Tian

Research output: Contribution to journalArticleResearchpeer-review

45 Citations (Scopus)

Abstract

In this paper we present the composite Euler method for the strong solution of stochastic differential equations driven by d-dimensional Wiener processes. This method is a combination of the semi-implicit Euler method and the implicit Euler method. At each step either the semi-implicit Euler method or the implicit Euler method is used in order to obtain better stability properties. We give criteria for selecting the semi-implicit Euler method or the implicit Euler method. For the linear test equation, the convergence properties of the composite Euler method depend on the criteria for selecting the methods. Numerical results suggest that the convergence properties of the composite Euler method applied to nonlinear SDEs is the same as those applied to linear equations. The stability properties of the composite Euler method are shown to be far superior to those of the Euler methods, and numerical results show that the composite Euler method is a very promising method.

Original languageEnglish
Pages (from-to)407-426
Number of pages20
JournalJournal of Computational and Applied Mathematics
Volume131
Issue number1-2
DOIs
Publication statusPublished - 1 Jun 2001

Keywords

  • Composites Euler method
  • Euler methods
  • Numerical stability
  • Stochastic differential equations

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