使用精确的有限差方法解决异常扰乱的弗雷德霍尔姆整微分方程.
Solomon Regasa Badeye1, Mesfin Mekuria Woldaregay2, Tekle Gemechu Dinka1
1Department of Applied Mathematics, Adama Science and Technology University, Adama, Ethiopia.
BMC research notes
|September 28, 2023
概括
这项研究引入了一种新型的数值方案,用于异常扰乱的弗雷德霍尔姆整微分方程. 该方法实现了二次统一的融合,通过理论分析和计算结果进行验证.
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:
- 奇异扰乱的弗雷德霍尔姆整微分方程带来了重大的数值挑战.
- 现有的方法可能会在各种参数值的统一收方面扎.
研究的目的:
- 设计和分析一个新型的数值方案,用于单一扰乱的弗雷德霍尔姆整微分方程.
- 确保拟议方法的稳定性和统一的趋同.
主要方法:
- 该方案结合了对差分部分的精确 (非标准) 有限差方法.
- 复合的辛普森的1/3规则用于不可分割的部分.
主要成果:
- 稳定性和均收被严格分析,使用溶液和截断误差极限.
- 计算结果证明了模型示例的第二阶统一收.
- 该方法显示了理论预测和数值结果之间的绝佳一致性.
结论:
- 拟议的数值方案是有效和准确的解决目标方程.
- 该方法在不同的扰动参数和网格大小中表现出强大的性能.
- 这项工作为这些复杂方程的数值解决提供了有价值的工具.
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