General order conditions for stochastic partitioned Runge-Kutta methods

被引：6
|
作者：
Anmarkrud, Sverre [1 ]
Debrabant, Kristian [2 ]
Kvaerno, Anne [3 ]
机构：
[1] Norwegian Univ Life Sci, Fac Environm Sci & Nat Resource Management, N-1433 As, Norway
[2] Univ Southern Denmark, Dept Math & Comp Sci, DK-5230 Odense M, Denmark
[3] Norwegian Univ Sci & Technol, Dept Math Sci, N-7491 Trondheim, Norway
来源：
BIT NUMERICAL MATHEMATICS | 2018年 / 58卷 / 02期
关键词：
Stochastic differential equations; Stochastic partitioned Runge-Kutta methods; Stochastic B-series; ROOTED TREE ANALYSIS; DIFFERENTIAL-EQUATIONS; HAMILTONIAN-SYSTEMS; B-SERIES; MULTIPLICATIVE NOISE; QUADRATIC-INVARIANTS; TAYLOR EXPANSIONS; NUMERICAL-METHODS; SCHEME;
D O I：
10.1007/s10543-017-0693-6
中图分类号：
TP31 [计算机软件];
学科分类号：
081202 ; 0835 ;
摘要：
In this paper stochastic partitioned Runge-Kutta (SPRK) methods are considered. A general order theory for SPRK methods based on stochastic B-series and multicolored, multishaped rooted trees is developed. The theory is applied to prove the order of some known methods, and it is shown how the number of order conditions can be reduced in some special cases, especially that the conditions for preserving quadratic invariants can be used as simplifying assumptions.
引用
收藏
页码：257 / 280
页数：24
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