Advanced research on stochastic Runge-Kutta methods

2014 Fiscal Year Final Research Report

• Project/Area Number: 23540143
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Kyushu Institute of Technology
• Principal Investigator: KOMORI YOSHIO 九州工業大学, 大学院情報工学研究院, 准教授 (20285430)
• Research Collaborator: BURRAGE Kevin オックスフォード大学, コンピューティングラボラトリー, 教授 ; BUCKWAR Evelyn ヨハネスケプラー大学, 確率解析学研究所, 教授 ; TOCINO Angel サラマンカ大学, 数学科, 准教授 ; COHEN David ウメオ大学, 数学科, 講師
• Project Period (FY): 2011-04-28 – 2015-03-31
• Keywords: 数値解法 / 確率微分方程式 / 数値的安定性 / 数値シミュレーション / 生化学反応

Outline of Final Research Achievements

We have derived new numerical methods for stochastic differential equations, which are ordinary differential equations with noise terms. For ordinary differential equations, there are well-known good methods, whose computational costs are relatively low and which can avoid numerical errors’ increasing. In the present study, we have succeeded in developing them into ones for stochastic differential equations, while keeping their advantages. As a practical example, we have applied our methods for simulation of biochemical reaction system, and showed the good performance of them.

Free Research Field

数値解析