数字调查的奇异地扰乱时间滞后抛物线微分方程方程
Imiru Takele Daba1, Wondwosen Gebeyaw Melesse2, Fasika Wondimu Gelu2
1Department of Mathematics, Salale University, Fitche, Ethiopia.
Heliyon
|January 13, 2025
概括
本研究从数值上研究了一个具有时间滞后的异常扰乱的抛物线微分方程. 一种新的方法结合了theta方法和非标准的有限差异,通过理查德森推断来增强,显著改善了收顺序.
科学领域:
- 数字分析 数字分析
- 计算数学 计算数学 计算数学
- 微分方程 微分方程 微分方程
背景情况:
- 具有时间滞后的奇异扰乱的抛物线微分方程带来了重大的数值挑战.
- 准确和高效的数值方法对于解决这些复杂方程至关重要.
研究的目的:
- 为特定类微分方程开发和分析一个强大的数值方案.
- 提高现有数值方法的准确性和趋同率.
主要方法:
- 使用时间变量的theta方法进行分离.
- 应用非标准的有限差异方法进行空间离散.
- 利用理查德森推断来加速数值方案的收.
主要成果:
- 提出的数值方法有效地处理了方程的异常扰动性.
- 方法的组合和理查德森推断显著提高了收的顺序.
- 数字示例证实了开发方案的适用性和改进性能.
结论:
- 提出的数值方法提供了一个可靠和准确的解决方案,单一扰乱的抛物线微分方程与时间滞后.
- 在趋同顺序中取得的改进表明了拟议技术的有效性.
相关概念视频
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01:21Linear Approximation in Time Domain
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01:26Linear Approximation in Frequency Domain
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