对于卡瓦哈拉和罗斯纳乌-海曼非线性波相互作用的最小平方余功率序列解决方案与流体动力学的应用

相关实验视频

Updated: May 9, 2025

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

11.5K

A Hassan¹, A A M Arafa², S Z Rida³

¹Department of Science and Mathematical Engineering, Faculty of Petroleum and Mining Engineering, Suez University, Suez, Egypt. a.kamal@suezuni.edu.eg.

Scientific reports

|April 28, 2025

概括

本研究介绍了最小平方余力序列 (LSRPS) 方法,用于解决非线性分数微分方程. 与传统的剩余功率序列 (RPS) 方法相比,LSRPS方法提供了更快的融合和更好的准确性.

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:

分数级非线性微分方程模型复杂的现象.
像剩余功率序列 (RPS) 方法这样的现有方法在趋同速度和准确性方面存在局限性.
有效的数值技术对于解决这些方程至关重要.

研究的目的:

开发和介绍最小平方剩余功率序列 (LSRPS) 方法.
将LSRPS方法应用于非线性分数顺序卡瓦哈拉方程和罗塞纳乌-海曼方程的近似解.
为了证明LSRPS方法比标准RPS方法更高的趋同性和准确性.

主要方法:

该研究将剩余功率序列 (RPS) 技术与最小平方方法相结合.
使用基于卡普托的分数导数的功率序列扩展来近似解决方案.
函数的线性独立性是使用 Wronskian 确定值来验证的.
一个线性方程系统是通过最小平方方法来解决的.

主要成果:

与经典的RPS方法相比,LSRPS方法提供了与较少扩展项的近似解决方案.
拟议的方法表现出明显更快的收率.
数字结果证实了LSRPS方法的效率,准确性和快速融合.

结论:

LSRPS方法是解决非线性分数微分方程的一个有效和高效的技术.
这种方法在计算速度和准确性方面具有优势.
LSRPS方法为分析分数顺序非线性模型提供了一个有希望的替代方案.

关键词:

分数 Wronskian 的使用.分数衍生工具分数衍生工具.卡瓦哈拉方程是什么意思最小平方的近似值.数字结果的数值结果.剩余功率序列方法的方法罗斯纳乌-海曼方程

相关概念视频

01:26

The Power Flow Problem and Solution

135

Power flow problem analysis is fundamental for determining real and reactive power flows in network components, such as transmission lines, transformers, and loads. The power system's single-line diagram provides data on the bus, transmission line, and transformer. Each bus k in the system is characterized by four key variables: voltage magnitude Vk, phase angle δk, real power Pk, and reactive power Qk. Two of these four variables are inputs, while the...

135

01:26

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....

01:21

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...

01:27

Traveling Waves: Lossless Lines

106

The provided content explores the behavior of traveling waves on single-phase lossless transmission lines. It begins with a single-phase two-wire lossless transmission line of length Δx, characterized by a loop inductance LH/m and a line-to-line capacitance C F/m. These parameters result in a series inductance LΔx and a shunt capacitance CΔx.

106

01:18

Newtonian Fluid: Problem Solving

135

Newtonian fluids exhibit a constant viscosity, meaning their shear stress and shear strain rate are directly proportional. This property ensures a predictable and stable response to applied forces, maintaining a linear relationship between force and flow. Examples include water, air, and light oils, consistently demonstrating this proportional behavior regardless of external conditions.
A velocity gradient forms within the fluid when a Newtonian fluid is placed between two parallel plates, with...

135

01:25

Poisson's And Laplace's Equation

2.5K

The electric potential of the system can be calculated by relating it to the electric charge densities that give rise to the electric potential. The differential form of Gauss's law expresses the electric field's divergence in terms of the electric charge density.