平衡隐性帕坦卡-欧勒方法用于生物调节系统的随机微分方程的正解
Aimin Chen1, Quanwei Ren2, Tianshou Zhou3
1School of Mathematics and Statistics, Henan University, Kaifeng 475001, China.
The Journal of chemical physics
|February 14, 2024
概括
我们开发了一种用于随机微分方程 (SDEs) 的新数值方法,可以保证积极的模拟,这对于建模生物系统至关重要. 这种平衡的隐性Patankar-Euler方法提高了稳定性和准确性.
科学领域:
- 数字分析 数字分析
- 计算数学是指计算数学.
- 数学建模的数学建模
背景情况:
- 随机微分方程 (SDEs) 对于模拟具有不确定性的复杂系统至关重要.
- 现有的SDE数值方法可以产生非物理的负解,特别是在生物应用中.
- 在SDEs的数值模拟中确保积极性仍然是一个重大挑战.
研究的目的:
- 提出一种新的数值方法,即平衡隐性帕坦卡-欧勒方法,用于模拟SDEs.
- 确保数值解决方案保持正数,解决现有方法的局限性.
- 提高SDE模拟的稳定性和准确性,特别是对于需要正值的系统.
主要方法:
- 通过从显式方法中删除潜在的负项来开发平衡的隐性帕坦卡-欧勒方法.
- 纳入平衡条款来处理负值漂移和扩散条款.
- 稳定性分析将拟议的方法与现有的复合Patankar-Euler方法进行比较.
- 使用四种不同的SDE系统进行验证,以评估有效性,准确性和趋同.
主要成果:
- 拟议的平衡隐性帕坦卡-尤勒方法成功地确保了对SDEs的积极模拟.
- 该方法有效地解决了先前在Patankar随机方法中遇到的小分母除法问题.
- 与复合Patankar-Euler方法相比,稳定性分析显示出优越的稳定性特性.
- 数字实验证实了新方法的有效性,准确性和趋同性.
结论:
- 平衡的隐性帕坦卡-欧勒方法是模拟需要积极解决方案的SDEs的有效和高效方法.
- 这种方法特别适合模拟生物调节系统,其中正性是必不可少的.
- 该技术提供了更好的稳定性和准确性,使其成为计算科学中一个有价值的工具.
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