哈尔波束方法用于解决线性分数弗雷德霍尔姆整微分方程的合系统的类
Amer Darweesh1, Kamel Al-Khaled1, Omar Abu Al-Yaqeen1
1Department of Mathematics and Statistics, Jordan University of Science & Technology, Irbid, Jordan.
Heliyon
|October 9, 2023
概括
本研究介绍了哈尔波段方法和拉普拉斯哈尔波段方法,用于解决线性分数弗雷德霍尔姆整微分方程. 这些技术有效地将复杂的系统减少到可解决的代数方程中,提供准确和快速的近似解决方案.
科学领域:
- 数字分析 数字分析
- 应用数学 应用数学 应用数学
- 分数微积分的微积分计算.
背景情况:
- 分数整微分方程在寻找准确的解决方案方面存在重大挑战.
- 在科学和工程中,近似方法对于解决复杂的数学模型至关重要.
- 哈尔波纹法为简化此类方程提供了一个有前途的方法.
研究的目的:
- 开发和介绍线性分数弗雷德霍尔姆整微分方程的合系统的近似解决方案.
- 引入一种增强的数值技术,拉普拉斯哈尔波纹法,以提高准确性和效率.
- 通过说明性示例验证拟议的方法.
主要方法:
- 哈尔波纹方法的应用,将整微分方程转换为代数系统.
- 将拉普拉斯变换运算符与哈尔波段方法集成,以创建拉普拉斯哈尔波段方法.
- 解决得到的代数方程系统以获得近似的解决方案.
主要成果:
- 哈尔波纹法有效地将复杂的分数整微分数系统减少到可管理的代数系统.
- 拉普拉斯哈尔波段方法与标准的哈尔波段方法相比,显示出更高的准确性和更短的计算时间.
- 数字示例证实了两种拟议方法的有效性,效率和适用性.
结论:
- 哈尔波纹法及其拉普拉斯变形变体为线性分数弗雷德霍尔姆整微分方程提供了强大的和高效的数值解决方案.
- 这些方法为研究人员和从业人员提供了有价值的工具,这些研究人员和从业人员处理的是分数微积分模型.
- 提出的技术是准确的,高效的,并可用于实际应用的计算可行.
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