一些近似结果对随机分数顺序进化方程的温和解决方案的近似结果,这些方程是由高斯噪声驱动的
K Fahim1, E Hausenblas2, M Kovács3,4,5
1Department of Mathematics, Institut Teknologi Sepuluh Nopember, Kampus ITS Sukolilo, Surabaya, 60111 Indonesia.
Stochastic partial differential equations : analysis and computations
|August 8, 2023
概括
我们分析了随机积方程与高斯噪声的空间近似质量. 本文提供了使用光谱加勒金和有限元素方法对随机分数局部微分方程的误差估计.
科学领域:
- 数字分析 数字分析
- 随机局部微分方程 随机局部微分方程
- 计算数学是指计算数学.
背景情况:
- 卷积类型的随机积分方程与高斯噪声对于建模复杂系统至关重要.
- 这些方程出现在随机分数顺序部分微分方程 (SPDEs) 和经典SPDEs的温和解中.
- 抛物线类型的问题通常在它们的决定性演变运算符中表现出平滑性质,这是本研究的关键要求.
研究的目的:
- 为了研究随机积方程与高斯噪声的空间近似的质量.
- 根据确定性误差率来推导路径上的霍尔德规范误差估计.
- 改进现有的恒定热方程的结果.
主要方法:
- 对卷积类型的随机积分方程的分析.
- 使用不光滑的数据估计对确定性误差运算符及其衍生品.
- 应用空间分离技术,特别是光谱加勒金方法和有限元素.
主要成果:
- 对于随机积方程的路径Hölder规范中确定的误差估计.
- 证明近似率与确定性错误率直接相关.
- 对随机热方程取得了改进的结果.
结论:
- 该研究为分析随机积分方程的空间近似质量提供了一个强大的框架.
- 这些发现适用于各种随机局部微分方程,包括分数顺序方程.
- 开发的方法为数值解决方案提供了更高的准确性和效率.
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