High Weak Order Methods for Stochastic Differential Equations Based on Modified Equations
High Weak Order Methods for Stochastic Differential Equations Based on Modified Equations
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DOI：
10.1137/110846609
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发表时间：
2012-06
期刊：
影响因子：
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通讯作者：
A. Abdulle;David Cohen;G. Vilmart;K. Zygalakis
中科院分区：
文献类型：
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作者：
A. Abdulle;David Cohen;G. Vilmart;K. Zygalakis
受修正微分方程理论最新进展的启发，我们提出了一种构造高弱阶数值积分器的新方法，用于随机微分方程的时间积分。该方法通过弱二阶新方法的构造进行了说明，特别是非常适合刚性（均方稳定）随机问题的半隐式积分器，以及精确守恒随机动力系统的所有二次一阶积分的隐式积分器。数值例子证实了理论结果并显示了我们方法的多功能性。
Inspired by recent advances in the theory of modified differential equations, we propose a new methodology for constructing numerical integrators with high weak order for the time integration of stochastic differential equations. This approach is illustrated with the constructions of new methods of weak order two, in particular, semi-implicit integrators well suited for stiff (mean-square stable) stochastic problems, and implicit integrators that exactly conserve all quadratic first integrals of a stochastic dynamical system. Numerical examples confirm the theoretical results and show the versatility of our methodology.