Generalized two-step Maruyama methods for stochastic differential equations

Quanwei Ren and Hongjiong Tian

Applied Mathematics and Computation, 2018, vol. 332, issue C, 48-57

Abstract: In this paper, we propose generalized two-step Maruyama methods for solving Itô stochastic differential equations. Numerical analysis concerning consistency, convergence and numerical stability in the mean-square sense is presented. We derive sufficient and necessary conditions for linear mean-square stability of the generalized two-step Maruyama methods. We compare the stability region of the generalized two-step Maruyama methods of Adams type with that of the corresponding two-step Maruyama methods of Adams type and show that our proposed methods have better linear mean-square stability. A numerical example is given to confirm our theoretical results.

Keywords: Stochastic differential equation; Mean-square consistency; Mean-square convergence; Mean-square stability; Generalized two-step Maruyama method; Adams method (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:332:y:2018:i:c:p:48-57

DOI: 10.1016/j.amc.2018.03.003

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