一个强大的方法来计算分数级二维赫尔姆霍尔茨方程的解
Muhammad Nadeem1, Zitian Li2, Devendra Kumar3
1School of Mathematics and Statistics, Qujing Normal University, Qujing, 655011, China. nadeem@mail.qjnu.edu.cn.
Scientific reports
|February 20, 2024
概括
本研究介绍了埃尔扎基变换剩余功率序列方法 (ET-RPSM) 用于解决分数级赫尔姆霍尔茨方程,这对于波传播和声学至关重要. 这种新的方法通过代序列有效地提供准确的分析解决方案.
科学领域:
- 应用数学 应用数学 应用数学
- 数学物理学的数学物理.
- 波浪传播建模的模拟.
背景情况:
- 赫尔姆霍尔茨方程对于模拟波浪现象至关重要,包括水下声学和海洋波浪行为.
- 准确的分析解决方案对于理解各种环境中的波传播至关重要.
- 分数阶微分方程为复杂的波动力学提供了更精确的模型.
研究的目的:
- 引入和验证埃尔扎基变换剩余功率序列方法 (ET-RPSM) 对于分数级赫尔姆霍尔茨方程.
- 为了证明该方法在使用卡普托感应处理分数导数方面的能力.
- 展示拟议分析技术的效率和准确性.
主要方法:
- 将埃尔扎基变换 (ET) 与剩余功率序列方法 (RPSM) 结合起来.
- 使用ET将分数赫尔姆霍尔茨方程转换为复杂关系.
- 应用RPSM从复发关系中生成一个代序列解决方案.
主要成果:
- ET-RPSM成功地为分数级赫尔姆霍尔茨方程提供分析解决方案.
- 该方法在几次代内证明了对确切解决方案的快速收.
- 数字应用证实了拟议方案的效率和真实性.
结论:
- ET-RPSM是一种有效且可靠的技术,用于解决分数级赫尔姆霍尔茨方程.
- ET和RPSM的集成提供了一种新的方法,用于分数计算中的分析解决方案.
- 该方法能够处理分数顺序并产生快速,准确的结果,这突显了它在波传播研究中的重要性.
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