Partial Differential Equations in Applied Mathematics最新文献_第10页

Analysis of fractional viewpoints on the Jaulent–Miodek and Whitham–Broer–Kaup coupled equations Jaulent-Miodek和Whitham-Broer-Kaup耦合方程的分数视点分析

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2025-06-27 DOI: 10.1016/j.padiff.2025.101243

Sachit Kumar , Varun Joshi , Mamta Kapoor

In this work, we use the Caputo fractional calculus to methodically examine the Coupled Jaulent–Miodek (CJM) fractional equation and the fractional Whitham–Broer–Kaup (WBK) system. The Sumudu residual power series approach and the Sumudu iteration transform method are used to analyze the nonlinear fractional differential equation systems, providing a comprehensive analytical analysis. The Sumudu iteration transform approach is used to achieve the fractional WBK system’s dynamics, as well as the Sumudu power series residual approach is utilized to investigate the CJM equation’s behavior for fractions. We thoroughly examine their interactions using known solutions, using both symbolic calculations and numerical simulations. This leads to the identification of new solutions and the clarification of the way in which certain systems of fractions behave in terms of the operator of Caputo. The outcomes demonstrate the efficacy of the strategies used to decipher the intricate dynamics of fractional nonlinear systems by demonstrating a strong convergence agreement between analytical and numerical solutions.

在这项工作中，我们使用Caputo分数微积分系统地检查了耦合Jaulent-Miodek （CJM）分数方程和分数Whitham-Broer-Kaup （WBK）系统。采用Sumudu残差幂级数法和Sumudu迭代变换法对非线性分数阶微分方程系统进行了分析，提供了全面的分析方法。采用Sumudu迭代变换方法实现分数阶WBK系统的动力学，并利用Sumudu幂级数残差方法研究分数阶CJM方程的行为。我们使用已知的解决方案，使用符号计算和数值模拟，彻底检查它们的相互作用。这导致了新的解决方案的识别，并澄清了某些分数系统在卡普托算子方面的行为方式。结果表明，通过证明在解析解和数值解之间具有很强的收敛性，用于破译分数阶非线性系统的复杂动力学的策略的有效性。

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引用次数: 0

Mathematical model of Cynodon Dactylon’s allelopathic effect on perennial ryegrass for exploring plant-plant interactions based upon ordinary differential equations 基于常微分方程的Cynodon Dactylon化感作用对多年生黑麦草的数学模型研究

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2025-06-27 DOI: 10.1016/j.padiff.2025.101254

Dipesh , Pankaj kumar , Anjori Sharma

In this paper, a mathematical model and analysis is proposed to study the stimulatory allelopathic impact of cynodon dactylon on perennial ryegrass using ordinary differential equations. Equilibrium points and biological interpretation is analyzed using the Routh-Hurwitz theorem. Allelopathic produces synergistic effects between two plants that can result in apparent competition for space, nutrients, water and growth of the plant or apparent organisms depending on how the life cycles of their shared exploiters and/or commensal are influenced by inducing morphological, physiological, biochemical and chemical changes in plants. Plants are competing for space, which is required for proper growth and development of roots. Based on spacing allelopathic effect is very less as space increases in respect of root length and root branches increase. These allelopathy biochemicals are used for pest management. Whenever the behaviors of exploiters and commensals respond to induce changes in comparative plant numbers, indirect -interactions among plants arise. The Mann-Kendall, MK test, Bartletts test, and Anova test is used to analyze the data and numerical simulation. Also, the main objective of this research article allelopathic impact of plant-to-plant interaction research plays an important role in climate action and life cycle on land.

本文利用常微分方程，建立了犬齿草对多年生黑麦草刺激化感作用的数学模型并进行了分析。利用劳斯-赫维茨定理分析了平衡点和生物学解释。化感作用在两种植物之间产生协同效应，根据植物形态、生理、生化和化学变化对共同利用者和/或共生者的生命周期的影响，可以导致植物或表观生物对空间、养分、水分和生长的明显竞争。植物在争夺空间，这是根系正常生长和发育所必需的。基于间距的化感效应随根长和根枝间距的增加而减小。这些化感生物化学物质用于害虫管理。每当利用者和共生者的行为引起比较植物数量的变化时，植物间就会产生间接相互作用。采用Mann-Kendall检验、MK检验、Bartletts检验和Anova检验对数据进行分析和数值模拟。植物间化感作用的研究在气候作用和陆地生命周期中发挥着重要作用。

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引用次数: 0

The impact of carbon nanotubes (CNT) on heat generation and absorption, the behaviour of water and blood suspensions in an inclined channel with a porous matrix 碳纳米管（CNT）对热产生和吸收的影响，水和血液悬浮液在多孔基质倾斜通道中的行为

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2025-06-26 DOI: 10.1016/j.padiff.2025.101241

Mangala Kandagal , Ramesh Kempepatil , Jagadish V. Tawade , Nodira Nazarova , Manish Gupta , M. Khan

The study investigates the heat generation and absorption of engine oil, human blood and single wall carbon Nano tube (SWCNT) in an inclined channel filled with a porous matrix. Two regions are considered, both regions are of porous medium. Due to their enhanced thermal conductivity, are utilized to improve heat transfer efficiency in various applications. Formulation of the problem is framed using conservation of mass, energy and momentum in both regions. The flow of oil, human blood through a porous medium is analysed, considering the effects of both heat generation and absorption within the system. Key parameters such as the inclination angle of the channel, the porosity and the type of fluids are examined to understand their impact on the overall heat transfer process and velocity. To solve the problem regular perturbation method is applied for non-dimensional quantities; The presence of CNTs significantly improves the thermal conductivity of both engine oil and blood suspensions, leading to improved heat dissipation or absorption capabilities, which are influenced by the inclination and the porous structure. This study offers valuable insights into fluid flow processes in the human body using Nanotubes. Influence of CNTs on the fluid flow of human body and heat generation/absorption with porous matrix in both regions is unsolved problem.

研究了发动机机油、人体血液和单壁碳纳米管（SWCNT）在多孔基质填充的倾斜通道中的产热和吸热特性。考虑两个区域，两个区域均为多孔介质。由于其增强的导热性，在各种应用中被用来提高传热效率。问题的表述是利用两个区域的质量、能量和动量守恒来构建的。考虑到系统内热的产生和吸收的影响，分析了油、人的血液在多孔介质中的流动。研究了通道倾角、孔隙度和流体类型等关键参数，以了解它们对整体传热过程和速度的影响。为解决这一问题，对无量纲量采用正则摄动法；CNTs的存在显著提高了机油悬浮液和血液悬浮液的导热性，从而提高了其散热或吸收能力，而这些能力受倾斜和多孔结构的影响。这项研究为利用纳米管研究人体流体流动过程提供了有价值的见解。CNTs对人体流体流动以及多孔基质在这两个区域产生/吸收热量的影响是尚未解决的问题。

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引用次数: 0

Detailed analysis under fully constrained and relaxed boundary conditions of linear fields in the vicinity of a corner 角附近线性场在完全约束和松弛边界条件下的详细分析

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2025-06-26 DOI: 10.1016/j.padiff.2025.101244

Ayelet Goldstein, Ofer Eyal, Jorge Berger

This work examines the behavior of fields near corners under various boundary conditions (BCs), focusing on singularities arising from fully constrained and relaxed BCs. We analyze this behavior across diverse physical systems governed by similar equations, including electromagnetism, superconductivity, and two-phase fluid flow. The corner geometry presents a challenge due to potentially diverging field solutions as the corner is approached (r

\to

0). This motivates the investigation of relaxed BCs, which regularize the field by introducing a characteristic length (Ls) that relates the field’s value to its normal derivative at the boundary.

We explore both single-medium (single-phase) and double-medium (two-phase) systems. While prior research has addressed relaxed BCs in specific contexts, their application to corners, particularly in diverse physical systems, remains under-explored. We develop a series solution method to analyze the field behavior near the corner under different BCs. Concrete examples illustrate the theoretical framework, examining both fully constrained and relaxed scenarios. The implications of this work extend to fields such as fluid mechanics, electromagnetism, and heat transfer.

本研究考察了不同边界条件下拐角附近场的行为，重点研究了完全约束和松弛边界条件下产生的奇点。我们分析了由类似方程控制的不同物理系统的这种行为，包括电磁学，超导性和两相流体流动。当拐角接近（r→0）时，由于潜在的发散场解，拐角的几何形状带来了挑战。这激发了对松弛bc的研究，它通过引入一个特征长度（Ls）来使场正则化，该特征长度将场的值与其在边界处的法向导数联系起来。我们探索单介质（单相）和双介质（两相）系统。虽然之前的研究已经在特定的环境中解决了松弛的bc，但它们在角落的应用，特别是在不同的物理系统中，仍然没有得到充分的探索。我们提出了一种级数解的方法来分析不同bc下的拐角附近的场行为。具体的例子说明了理论框架，检查了完全约束和放松的场景。这项工作的意义延伸到流体力学、电磁学和传热等领域。

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引用次数: 0

An iterative method for solving sparse linear algebraic systems with continuum solution dependent right-hand side for elliptic partial differential equations 求解椭圆型偏微分方程右侧连续解相关稀疏线性代数系统的迭代方法

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2025-06-21 DOI: 10.1016/j.padiff.2025.101236

Sudipta Lal Basu , Kirk M. Soodhalter , Breiffni Fitzgerald , Biswajit Basu

Krylov subspace iterative methods such as bi-conjugate gradients stabilized (BiCGStab) to approximately solve sparse linear algebraic systems are well known. However, there are certain instances in real-world engineering applications with underlying governing partial differential equation where the discretized right-hand side can only be exactly determined using the unavailable continuum solution. In such cases, an iterative method such as BiCGStab may not converge to a physically correct solution or may diverge completely. Such a method must be modified to accommodate inexact knowledge of the discrete right-hand side, using an updating scheme as the iteration proceeds. In this paper, we present such an updating strategy for physical problems governed by elliptic partial differential equations. This strategy must be performed in a numerically stable manner, which we also discuss. We present this as a modified BiCGStab iteration and investigate its effectiveness on both test problems, wherein it is shown to perform well and agrees with the analytical solutions, and on some more realistic problems arising in the study of Hele-Shaw flow, composite materials and power generation from wind farms.

Krylov子空间迭代方法如双共轭梯度稳定（BiCGStab）近似求解稀疏线性代数系统是众所周知的。然而，在现实世界的工程应用中，存在某些具有潜在控制偏微分方程的实例，其中离散的右侧只能使用不可用的连续介质解来精确确定。在这种情况下，像bicstab这样的迭代方法可能不会收敛到物理上正确的解决方案，或者可能完全发散。这种方法必须进行修改，以适应离散右边的不精确知识，并在迭代进行时使用更新方案。在本文中，我们提出了一种求解椭圆型偏微分方程物理问题的更新策略。此策略必须以数值稳定的方式执行，我们也将讨论这一点。我们将其作为改进的BiCGStab迭代，并研究其在两个测试问题上的有效性，其中它显示出良好的性能并与解析解一致，以及在研究Hele-Shaw流，复合材料和风力发电场发电中出现的一些更现实的问题。

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引用次数: 0

An enhanced Artificial Neural Network approach for solving nonlinear fractional-order differential equations 求解非线性分数阶微分方程的增强人工神经网络方法

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2025-06-18 DOI: 10.1016/j.padiff.2025.101230

Nikhil Sharma , Sunil Joshi , Pranay Goswami

This paper introduces a hybrid Chebyshev Collocation Method (CCM) and Artificial Neural Network (ANN) approach to address the computational challenges of nonlinear Caputo fractional differential equations. The purpose is to improve accuracy for static solutions by approximating the fractional derivative spatially. The methodology leverages CCM for spatial discretization and ANN for residual minimization, achieving low MSEs (e.g.,

1 0^{- 5}

) in three examples. The findings confirm improved convergence with increasing node count, with implications for efficient fractional PDE solvers. The novelty lies in the static CCM+ANN integration, offering a practical alternative to dynamic methods.

本文介绍了一种混合Chebyshev配置法（CCM）和人工神经网络（ANN）方法来解决非线性Caputo分数阶微分方程的计算难题。目的是通过在空间上近似分数阶导数来提高静态解的精度。该方法利用CCM进行空间离散化，利用ANN进行残差最小化，在三个示例中实现了低mse（例如10−5）。研究结果证实，随着节点数的增加，收敛性得到改善，这对有效的分数阶PDE求解器具有重要意义。新颖之处在于静态CCM+ANN集成，为动态方法提供了一种实用的替代方案。

引用次数: 0

Fractional modelling of heat transfer through porous media for incompressible MHD fluid flow with laplace transform approach 用拉普拉斯变换方法模拟不可压缩MHD流体在多孔介质中的传热

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2025-06-18 DOI: 10.1016/j.padiff.2025.101242

Muhammad Kazim, Mubashir Abbas, Safder Hussain, Munawwar Ali Abbas

In this paper, we investigate a fractional model of an incompressible and unstable MHD viscous fluid with heat transfer pass across a porous medium. To quantify this, we used a vertical plate with a fluid connected to it. When an angled magnetic field is supplied, the plate moves in its own plane. The required nonlinear partial differential equations are used to convert the governing equations into a non-dimensional form. To find the solution of the simplified nonlinear partial differential equations, the Constant Proportional Caputo fractional derivatives are utilized. The Laplace transform techniques are used to simplify the non-dimensional governing equations of the model and the boundary conditions we discovered explicit formulations for each field. The resultant equation is solved for momentum and energy, and the solutions are given as series. The performance of velocity and temperature values are graphically plotted using MATHCAD software. In numerical simulation, the Local Skin fraction and local Nusselt number are considered and evaluated additionally. It has been concluded that the fluid’s temperature and velocity decreases by increasing the value of fractional parameter. It has also been found that the velocity and temperature increase with increasing values of

Q_{0}

.

在本文中，我们研究了一个分数模型的不可压缩和不稳定的MHD粘性流体传热通过多孔介质。为了量化这一点，我们使用了一个与流体相连的垂直板。当提供有角度的磁场时，板在自己的平面内运动。利用所需的非线性偏微分方程将控制方程转化为无量纲形式。利用常比例卡普托分数阶导数求简化非线性偏微分方程的解。利用拉普拉斯变换技术简化了模型的无量纲控制方程，并发现了每个场的显式边界条件。求解了结果方程的动量和能量，并以级数形式给出了解。利用MATHCAD软件绘制了速度和温度值的性能图。在数值模拟中，考虑了局部Skin分数和局部Nusselt数，并对其进行了评价。结果表明，分数参数的增大会降低流体的温度和速度。速度和温度随q0的增大而增大。

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引用次数: 0

Dynamical analysis and numerous signal transmission behavior of the nonlinear Pochhammer-Chree (PC) model via two consistent schemes 两种一致方案下非线性Pochhammer-Chree （PC）模型的动力学分析及多信号传输行为

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2025-06-16 DOI: 10.1016/j.padiff.2025.101248

M. Al-Amin , M․Nurul Islam , M․Ali Akbar

This investigation conducts a comprehensive analytical analysis of the renowned nonlinear Pochhammer-Chree (PC) model by utilizing two efficient methods. The nonlinear PC model stands as a robust tool for the analysis of movement of traveling waves in a substantially long cylindrical rod with a circular cross-section, and longitudinal wave such as sound and particle wave propagation through elastic medium. The PC model also plays very important role in explaining various natural and engineering applications. To establish these results, we employ the generalized exponential rational function (GERF) method and the auxiliary equation (AE) method. The obtain results uncover numerous secrete dynamical characteristics of the model. Here, we also examine the influences of wave propagation velocity parameter on the attained solutions to understand the inner mechanism and dynamical signal transmission behavior of the related phenomenon. The gestures of obtained results are explained by representing the 3-dimensional (3D) and 2-dimensional (2D) shapes. The attained solutions demonstrate that the employed techniques are straightforward, reliable, functional and more effective to extracting soliton solutions of numerous nonlinear models.

本研究利用两种有效的方法对著名的非线性Pochhammer-Chree （PC）模型进行了全面的分析。非线性PC模型是分析行波在具有圆形截面的长圆柱棒中的运动，以及纵波如声波和粒子波在弹性介质中的传播的可靠工具。PC模型在解释各种自然和工程应用方面也起着非常重要的作用。为了证明这些结果，我们采用了广义指数有理函数（GERF）方法和辅助方程（AE）方法。所得结果揭示了模型的许多秘密动力学特性。本文还考察了波传播速度参数对所得解的影响，以了解相关现象的内在机制和动态信号传输行为。通过表示三维（3D）和二维（2D）形状来解释所获得结果的手势。得到的解表明，所采用的方法简单、可靠、有效，可用于提取大量非线性模型的孤子解。

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引用次数: 0

Exploring mixed convection in porous media: Thermal and flow behaviour 探索多孔介质中的混合对流：热和流动行为

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2025-06-16 DOI: 10.1016/j.padiff.2025.101239

Shreedevi Kalyan , Mangala Kandagal , Jagadish V. Tawade , Nitin Satpute , M. Ijaz Khan , Nitiraj Kulkarni , Nargiza Kamolova , Manish Gupta

This study explores mixed convective flow within a porous medium, considering scenarios of heat generation or absorption. The focus is on solving the nonlinear differential equations that describe concentration, temperature, and velocity profiles, with graphical representations provided for each. Notably, this research addresses an area previously unexamined. By employing the regular perturbation method, solutions to the nonlinear ordinary differential equations, derived from the nondimensionalized governing equations, are achieved. Various factors significantly influence fluid flow parameters, revealing intriguing phenomena. The results offer valuable insights into velocity and temperature distributions across diverse porous characteristics, including thermal temperature, viscosity ratio, width ratio, conductivity ratio, and Grashof number. A decrease in velocity is observed due to factors such as the porous structure, viscosity variations, and conductance differences. Conversely, an increase in flow velocity is noted with higher Grashof numbers and width-to-height ratios.

本研究探讨了多孔介质内的混合对流，考虑了热产生或吸收的情况。重点是解决描述浓度、温度和速度分布的非线性微分方程，并为每个方程提供图形表示。值得注意的是，这项研究涉及了一个以前未被研究过的领域。利用正则摄动法，由无量纲化控制方程导出了非线性常微分方程的解。各种因素显著影响流体流动参数，揭示出有趣的现象。结果为不同孔隙特性（包括热温度、粘度比、宽度比、电导率比和Grashof数）的速度和温度分布提供了有价值的见解。由于多孔结构、粘度变化和电导差异等因素，可以观察到速度的降低。相反，随着格拉什夫数和宽高比的增加，流速也会增加。

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引用次数: 0

Peristaltic flow of nanofluid with temperature dependent viscosity in an annulus 具有温度依赖粘度的纳米流体在环空中的蠕动流动

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2025-06-16 DOI: 10.1016/j.padiff.2025.101240

Swathi H R , Indira Ramarao , Jagadeesha S , Ganesh Kumar K , Prakasha D G

Peristaltic flow in an annular region bounded by a concentric cylindrical tube is considered. The current study focuses on understanding enhancement of heat transfer in presence of nanoparticles. It also studies the effect of peristaltic motion on enhancement of heat transfer. The outer tube is subjected to a sinusoidal wave, and inner tube is rigid. Nanofluid has a variable viscosity which depends on temperature. Analytical solutions for temperature, velocity, and pressure gradient are evaluated and the effect of carbon nanotube is represented graphically. A method of regular perturbation is adopted to get an analytical solution. The impact of having single-walled carbon nanotubes (SNT) and multi-walled carbon nanotubes (MNT) on the parameters like pressure gradient, temperature, and velocity. Long wavelength approximation is assumed on a low Reynold’s flow. The impact of inner tube radius, amplitude of sinusoidal wave, and rate of flow on pressure gradient are analyzed for both SNT and MNT.

考虑了以同心圆柱形管为界的环形区域内的蠕动流动。目前的研究重点是了解纳米颗粒存在时传热的增强。研究了蠕动运动对强化换热的影响。外管受到正弦波的作用，而内管是刚性的。纳米流体的粘度随温度的变化而变化。评价了温度梯度、速度梯度和压力梯度的解析解，并用图形表示了碳纳米管的影响。采用正则摄动法得到解析解。单壁碳纳米管（SNT）和多壁碳纳米管（MNT）对压力梯度、温度和速度等参数的影响。在低雷诺数流条件下，假定长波长近似。分析了内管半径、正弦波振幅和流速对SNT和MNT压力梯度的影响。

引用次数: 0