Strong first order S-ROCK methods for stochastic differential equations

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics Pub Date : 2013-04-01 DOI:10.1016/j.cam.2012.10.026

Yoshio Komori , Kevin Burrage

引用次数: 23

Abstract

Explicit stochastic Runge–Kutta (SRK) methods are constructed for non-commutative Itô and Stratonovich stochastic differential equations. Our aim is to derive explicit SRK schemes of strong order one, which are derivative free and have large stability regions. In the present paper, this will be achieved by embedding Chebyshev methods for ordinary differential equations in SRK methods proposed by Rößler (2010). In order to check their convergence order, stability properties and computational efficiency, some numerical experiments will be performed.

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随机微分方程的强一阶S-ROCK方法

构造了非交换Itô和Stratonovich随机微分方程的显式随机龙格-库塔(SRK)方法。我们的目标是得到强一阶的显式SRK格式，它是无导数的，并且具有大的稳定区域。在本文中，这将通过在Rößler(2010)提出的SRK方法中嵌入常微分方程的Chebyshev方法来实现。为了检验它们的收敛阶、稳定性和计算效率，将进行一些数值实验。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Computational and Applied Mathematics 数学-应用数学

CiteScore

5.40

自引率

4.20%

发文量

437

审稿时长

3.0 months

期刊介绍： The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest. The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.