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带有光谱转移的切比舍夫聚合技术与剩余功率序列算法,用于时间分数问题

Saad Z Rida¹, Anas A M Arafa^2,3, Hussein S Hussein¹

¹Department of Mathematics, Faculty of Science, South Valley University, Qena, 83523, Egypt.

Scientific reports

|April 15, 2024

概括

这项研究引入了一种新方法,即用剩余功率序列算法 (CTSCSK-RPSA) 来解决复杂的分数局部微分方程 (PDEs) 的第二种切比舍夫转移的拼接技术. 开发的CTSCSK-RPSA方法在各种物理和工程问题上被证明是准确和高效的.

科学领域:

应用数学应用数学应用数学
数字分析数字分析
分数微积分的计算.

背景情况:

分数局部微分方程 (PDEs) 对于模拟复杂现象至关重要.
与非局部条件相结合的非线性时间分数超标和伪超标PDEs带来了重大分析挑战.
对于这些类型的问题,现有的数值方法可能缺乏准确性或效率.

研究的目的:

提出和解决两个特定的问题,涉及非线性时间分数的过度波动PDEs和时间分数的伪过度波动PDEs.
引入和验证第二种转移的切比舍夫与剩余功率序列算法 (CTSCSK-RPSA) 的拼接技术.
为拟议的数值方法提供详细的错误分析.

主要方法:

主要采用的方法是第二种转移的切比舍夫与剩余功率序列算法 (CTSCSK-RPSA) 的拼接技术.
这种技术将光谱方法与序列扩展方法相结合,以实现高效的计算.
该方法应用于解决非线性时间分数超波和伪超波PDE与非局部条件.

主要成果:

对于所呈现的小数 PDE 得到了数值解.
通过详细的错误分析,证明了CTSCSK-RPSA方法的准确性和效率.
使用CTSCSK-RPSA获得的数值结果与现有技术进行了比较,显示出具有竞争力的性能.

结论:

CTSCSK-RPSA是一种准确,简单和方便的方法,用于解决线性和非线性分数PDEs.
这种方法提供了一种可靠的方法来解决复杂的物理和工程问题.
详细的错误分析支持CTSCSK-RPSA对于分数微分方程的稳定性.

关键词:

分数衍生工具分数衍生工具.超标式方程与时间分数.数字结果. 数字结果.剩余功率序列算法剩余功率序列算法转移的切比舍夫多项式第二种.时间分数伪夸大方程时间分数伪夸大方程

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