Partial Differential Equations in Applied Mathematics最新文献

英文中文

Three-dimensional Darcy-forchheimer modelling of MHD hybrid nanofluid over rotating stretching/shrinking surface with Hamilton-Crosser and Yamada-Ota conductivity models 利用 Hamilton-Crosser 和 Yamada-Ota 传导模型对旋转拉伸/收缩表面上的 MHD 混合纳米流体进行三维达西-福克海默建模

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2024-10-22 DOI: 10.1016/j.padiff.2024.100973

Subhajit Panda , P.K. Pattnaik , S.R. Mishra , Surender Ontela

Instead of single nanoparticles, the combined effects of more than one solid nanoparticle have presented wide range of real-word application in several engineering as well as biomedical areas. The present analysis brings out a combined effect of Hamilton-Crosser and Yamada-Ota thermal conductivity models for the magnetohydrodynamic flow of hybridised fluid vi a rotating stretching/shrinking surface. The hybridised fluid comprised of silver and molybdenum tetrasulphide nanoparticle in association with the effect of Joule heating enriches the flow properties. Additionally, the Darcy-Forchheimer inertial drag with the impose of thermal radiation affecting the flow as well as heat transfer properties. The proposed mathematical model equipped with physical assumptions is transmuted into dimensionless form by utilizing similarity functions. Further, the traditional numerical technique is taken care of for the solution of the transmuted model equipped with diversified factors. The important characteristic of several factors are deployed graphically affecting various flow profiles. Finally, the outstanding features explored in the proposed investigation are stated as below; the comparative analysis reveals that, the heat transport properties became advanced in case of Hamilton-Crosser model rather than the Yamada-Ota conductivity model. However, the heat transportation rate is controlled by the increasing Eckert number but thermal radiation enhances it significantly.

与单个纳米粒子相比，多个固体纳米粒子的组合效应在多个工程和生物医学领域都有广泛的实际应用。本研究分析了汉密尔顿-克罗瑟（Hamilton-Crosser）和山田-太田（Yamada-Ota）热导率模型对旋转拉伸/收缩表面上的杂化流体磁流体流动的综合影响。由银和四硫化钼纳米粒子组成的杂化流体在焦耳加热的作用下丰富了流动特性。此外，达西-福克海默惯性阻力和热辐射也会影响流动和传热特性。利用相似函数将所提出的物理假设数学模型转化为无量纲形式。此外，还采用了传统的数值技术来求解包含多种因素的转化模型。多个因素的重要特征以图形方式显示出来，并对各种流动剖面产生影响。比较分析表明，与 Yamada-Ota 传导模型相比，Hamilton-Crosser 模型的热传导特性更为先进。然而，热传导率受艾克特数增大的控制，但热辐射会显著提高热传导率。

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引用次数: 0

Integrated Jacobi elliptic function solutions to the (3+1)-dimensional generalized Kadomtsev–Petviashvili equation by utilizing new solutions of the elliptic equation of order six 利用阶数为 6 的椭圆方程的新解，求 (3+1) 维广义卡多姆采夫-彼得维亚什维利方程的雅可比椭圆函数积分解

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2024-10-22 DOI: 10.1016/j.padiff.2024.100954

Ahmad H. Alkasasbeh , Belal Al-Khamaiseh , Ahmad T. Ali

In this research, the generalized

(3 + 1)

-dimensional Kadomtsev–Petviashvili equation (

(3 + 1)

-GKPE) that expresses various nonlinear phenomena was studied. An extended Jacobi elliptic function expansion method (JEFEM) was developed by considering new solutions for the Jacobi elliptic equation of order six. Then the extended method was applied to the

(3 + 1)

-GKPE, where new exact Jacobi elliptic function solutions were obtained. This equation is of particular interest as it required a special transformation in order to apply the JEFEM. Moreover, some of the solutions are shown graphically.

本研究对表达各种非线性现象的广义（3+1）维卡多姆采夫-彼得维亚什维利方程（(3+1)-GKPE）进行了研究。通过考虑六阶雅可比椭圆方程的新解，开发了扩展雅可比椭圆函数展开法（JEFEM）。然后，将扩展方法应用于 (3+1)-GKPE ，得到了新的精确雅可比椭圆函数解。该方程需要特殊的变换才能应用 JEFEM，因此特别引人关注。此外，其中一些解还以图形方式显示出来。

引用次数: 0

Impact of fractional and integer order derivatives on the (4+1)-dimensional fractional Davey–Stewartson–Kadomtsev–Petviashvili equation 分数和整数阶导数对 (4+1)-dimensional 分数 Davey-Stewartson-Kadomtsev-Petviashvili 方程的影响

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2024-10-21 DOI: 10.1016/j.padiff.2024.100966

Adil Jhangeer , Haiqa Ehsan , Muhammad Bilal Riaz , Abdallah M. Talafha

In this study, the closed-form wave solutions of the

(4 + 1)

-dimensional fractional Davey–Stewartson–Kadomtsev–Petviashvili equation are investigated using the modified auxiliary equation method and the Jacobi elliptic function method. In the analysis, two fractional derivatives known as M-truncated, beta and integer order derivative are used. The fractional-order partial differential equation is transformed into an integer-order ordinary differential equation by using the wave transformation, fractional derivatives, and integer-order derivatives. As a result, wave function solutions are found, including bell shape, W-shaped, composite dark-bright and periodic wave. The effects of free parameters on the amplitudes and wave behaviors are illustrated. It is demonstrated extensively that changes in the free parameters lead to changes in the wave amplitude. A comparison of solutions using the two types of fractional derivatives and the integer-order derivatives is included. The effects of the beta derivative, the M-truncated derivative and integer order derivative on the considered model are presented using 2D and 3D figures.

本研究采用修正辅助方程法和雅各比椭圆函数法研究了 (4+1)-dimensional 分数 Davey-Stewartson-Kadomtsev-Petviashvili 方程的闭式波解。分析中使用了两种分数导数，即 M 截断导数、β 阶导数和整阶导数。通过使用波变换、分数导数和整阶导数，分数阶偏微分方程被转化为整阶常微分方程。结果找到了波函数解，包括钟形波、W 形波、复合暗-亮波和周期波。说明了自由参数对振幅和波行为的影响。研究广泛证明，自由参数的变化会导致波幅的变化。比较了使用两种分数导数和整阶导数的解法。使用二维和三维图展示了贝塔导数、M 截断导数和整阶导数对所考虑模型的影响。

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引用次数: 0

Computing the Dirichlet-to-Neumann map via an integral equation with the adjoint generalized Neumann kernel 通过具有邻接广义诺伊曼核的积分方程计算狄利克特到诺伊曼映射

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2024-10-21 DOI: 10.1016/j.padiff.2024.100967

Samir Naqos , Ali H.M. Murid , Mohamed M.S. Nasser , Su Hoe Yeak

A new numerical method for computing the Dirichlet-to-Neumann map for Laplace’s equation in simply and multiply connected smooth domains is introduced. This method is based on an integral equation with the adjoint generalized Neumann kernel. Contrary to the classical approach which requires numerical differentiation in a post-processing step, our method allows computing the Dirichlet-to-Neumann map directly without the need of numerical differentiation in post-processing. The results of our numerical experiments demonstrate that the proposed method gives better accuracy and is more efficient than the classical approach for large problems with unbounded multiply connected domains.

介绍了一种计算简单和多重连接光滑域中拉普拉斯方程的 Dirichlet 到 Neumann 映射的新数值方法。该方法基于具有广义诺依曼核的积分方程。与需要在后处理步骤中进行数值微分的经典方法相反，我们的方法可以直接计算 Dirichlet 到 Neumann 地图，而无需在后处理中进行数值微分。我们的数值实验结果表明，对于无界多连通域的大型问题，所提出的方法比经典方法更准确、更高效。

引用次数: 0

A Galerkin finite element technique with Iweobodo-Mamadu-Njoseh wavelet (IMNW) basis function for the solution of time-fractional advection–diffusion problems 利用 Iweobodo-Mamadu-Njoseh 小波 (IMNW) 基函数的 Galerkin 有限元技术求解时间分数平流扩散问题

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2024-10-21 DOI: 10.1016/j.padiff.2024.100965

D.C. Iweobodo , G.C. Abanum , N.I. Ochonogor , J.S. Apanapudor , I.N. Njoseh

In this paper, the authors used wavelet-based Galerkin finite element technique constructed with Iweobodo-Mamadu-Njoseh wavelet as the basis function, for the numerical solution of time-fractional advection–diffusion equations. To achieve this, the authors used the Iweobodo-Mamadu-Njoseh wavelet as well as fractional calculus, wavelet and wavelet transform, and the Galerkin finite element technique. Also, time and space discretization in relation to the finite element technique were considered, followed by the steps in implementing numerical solutions to TFADE with the new technique. The new technique was considered in seeking numerical solutions of some Caputo type TFADE test problems, and the resulting numerical evidence displayed the effectiveness and accuracy of the method as the results obtained with the new method converged at a good pace to the exact solutions. The results obtained at different fractional order were also compared and the resulting evidence showed that at certain fractional value the convergence behavior displayed slight differences. Every numerical computation was done with the use of MAPLE 18 software.

本文作者采用以 Iweobodo-Mamadu-Njoseh 小波为基函数构建的基于小波的 Galerkin 有限元技术，对时间分数平流扩散方程进行数值求解。为此，作者使用了 Iweobodo-Mamadu-Njoseh 小波以及分数微积分、小波和小波变换以及 Galerkin 有限元技术。此外，还考虑了与有限元技术相关的时间和空间离散化问题，随后介绍了使用新技术对 TFADE 进行数值求解的步骤。在寻求一些卡普托类型 TFADE 试验问题的数值解时考虑了新技术，所得到的数值证据显示了该方法的有效性和准确性，因为用新方法得到的结果以很好的速度收敛到精确解。此外，还对不同分数阶数下的结果进行了比较，结果表明，在某些分数值下，收敛行为略有不同。所有数值计算均使用 MAPLE 18 软件完成。

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引用次数: 0

Brownian motion in a magneto Thermo-diffusion fluid flow over a semi-circular stretching surface 半圆拉伸面上磁热扩散流体流动中的布朗运动

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2024-10-20 DOI: 10.1016/j.padiff.2024.100970

Shankar Rao Munjam , D Gopal , N. Kishan , Shoira Formanova , K. Karthik , Furqan Ahmad , M. Waqas , Manish Gupta , M. Ijaz Khan

The current study explores the mass and heat transport analysis of a Casson liquid stream past a curved surface. The current model considers the effect of magnetic strength brought on by the strength of the applied uniform magnetic field. The significance of thermophoresis and Brownian motion are also taken into account using the Buongiorno nano-liquid model. The study of liquid flow over stretching sheets frequently addresses practical issues that have garnered significant attention from researchers due to their importance in various domains, including microfluidics, fibreglass production, manufacturing, transportation, metal extrusion, thermal insulation, glass production, paper manufacturing, and acoustic blasting. The governing partial differential equations (PDEs) are converted into ordinary differential equations (ODEs) using the similarity variables. These equations are numerically solved using the finite difference method (FDM). The concentration, temperature, and velocity graphs were produced by varying the different physical parameters. The upsurge in the magnetic parameter reduces the velocity profile. As the magnetic parameter increases, thermal and concentration profiles upsurge. The decrease in velocity profile can be seen as the Casson parameter rises. The intensification in values of thermophoretic parameter enhances the thermal and concentration profiles. The concentration and thermal profiles reduce as the curvature parameter upsurges.

本研究探讨了经过曲面的卡松液流的质量和热量传输分析。当前的模型考虑了外加均匀磁场强度带来的磁强效应。此外，还使用 Buongiorno 纳米液体模型考虑了热泳和布朗运动的重要性。对拉伸片上液体流动的研究经常涉及一些实际问题，这些问题在微流体、玻璃纤维生产、制造、运输、金属挤压、隔热、玻璃生产、造纸和声学爆破等各个领域都非常重要，因此受到了研究人员的极大关注。利用相似变量可将支配偏微分方程 (PDE) 转换为常微分方程 (ODE)。使用有限差分法（FDM）对这些方程进行数值求解。通过改变不同的物理参数，绘制出浓度、温度和速度曲线图。磁性参数的增加会降低速度曲线。随着磁参数的增加，热曲线和浓度曲线也随之上升。随着卡松参数的升高，速度曲线也随之降低。热泳参数值的增加会增强热曲线和浓度曲线。随着曲率参数的增大，浓度和热剖面也随之减小。

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引用次数: 0

Analysis of heat and mass transfer rates in conducting Casson fluid flow over an expanding surface considering Ohmic heating and Darcy dissipation effects 考虑欧姆加热和达西耗散效应的膨胀表面上传导卡松流体流动的传热和传质速率分析

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2024-10-20 DOI: 10.1016/j.padiff.2024.100972

Rupa Baithalu , S.R. Mishra , P.K. Pattnaik , Subhajit Panda

In a recent scenario, the flow of Casson fluid via porous media has practical applications in various engineering processes, such, as the design of cooling systems for electronic devices, oil recovery in porous reservoirs, and polymer extrusion processes, etc. The proposed investigation illustrates the thermal and solutal transfer rates in a conducting Casson fluid flow over an expanding surface. However, the emphasis goes to the behavior of the Ohmic heating and Darcy dissipation when considering the transverse magnetic field and porous matrix. The governing flow phenomena with their dimensional form are altered into a non-dimensional set of equations with the help of suitable similarity rules. Further, an adequate numerical simulation is adopted to solve the transformed equations using the in-house bvp4c function in MATLAB. The physical parameters involved in the flow problem and their behavior on the governing flow phenomena are presented graphically and described briefly. Prior to this investigation, the conformity of the current numerical output obtained for the heat transfer rate was validated with the earlier work with a good correlation. Moreover, the major outcomes are; the non-Newtonian Casson parameter retards the axial and transverse velocity profile and the shear rate also decreases significantly. The Eckert number caused by the inclusion of the dissipative heat encourages the fluid temperature throughout.

最近，卡松流体在多孔介质中的流动在各种工程过程中得到了实际应用，如电子设备冷却系统的设计、多孔储油层中的采油以及聚合物挤压过程等。拟议的研究说明了在膨胀表面上的导电卡松流体流中的热量和溶质传递率。不过，重点在于考虑横向磁场和多孔基质时的欧姆加热和达西耗散行为。在适当的相似性规则的帮助下，将具有维度形式的流动现象转化为非维度方程组。此外，还使用 MATLAB 中的内部 bvp4c 函数进行了充分的数值模拟，以求解转换后的方程。流动问题所涉及的物理参数及其对流动现象的影响以图表形式呈现，并进行了简要说明。在进行这项研究之前，已验证了当前获得的传热率数值输出与早期工作的一致性，两者之间具有良好的相关性。此外，主要结果是：非牛顿卡森参数会减缓轴向和横向速度曲线，剪切速率也会显著降低。由于包含了耗散热量，埃克特数提高了整个流体的温度。

{"title":"Analysis of heat and mass transfer rates in conducting Casson fluid flow over an expanding surface considering Ohmic heating and Darcy dissipation effects","authors":"Rupa Baithalu , S.R. Mishra , P.K. Pattnaik , Subhajit Panda","doi":"10.1016/j.padiff.2024.100972","DOIUrl":"10.1016/j.padiff.2024.100972","url":null,"abstract":"<div><div>In a recent scenario, the flow of Casson fluid via porous media has practical applications in various engineering processes, such, as the design of cooling systems for electronic devices, oil recovery in porous reservoirs, and polymer extrusion processes, etc. The proposed investigation illustrates the thermal and solutal transfer rates in a conducting Casson fluid flow over an expanding surface. However, the emphasis goes to the behavior of the Ohmic heating and Darcy dissipation when considering the transverse magnetic field and porous matrix. The governing flow phenomena with their dimensional form are altered into a non-dimensional set of equations with the help of suitable similarity rules. Further, an adequate numerical simulation is adopted to solve the transformed equations using the in-house bvp4c function in MATLAB. The physical parameters involved in the flow problem and their behavior on the governing flow phenomena are presented graphically and described briefly. Prior to this investigation, the conformity of the current numerical output obtained for the heat transfer rate was validated with the earlier work with a good correlation. Moreover, the major outcomes are; the non-Newtonian Casson parameter retards the axial and transverse velocity profile and the shear rate also decreases significantly. The Eckert number caused by the inclusion of the dissipative heat encourages the fluid temperature throughout.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 100972"},"PeriodicalIF":0.0,"publicationDate":"2024-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142529119","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Enhanced numerical techniques for solving generalized rotavirus mathematical model via iterative method and ρ-Laplace transform 通过迭代法和ρ-拉普拉斯变换求解广义轮状病毒数学模型的增强型数值技术

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2024-10-19 DOI: 10.1016/j.padiff.2024.100963

Rishi Kumar Pandey , Kottakkaran Sooppy Nisar

Rotavirus infection is a significant cause of severe diarrhea in infants and young children, contributing significantly to mortality rates worldwide. This research investigates a time fractional-order epidemic model for rotavirus under uncertain conditions, defined using the Katugampola fractional derivative (KFD). We employ a semi-analytic technique known as the Generalized Transform Variational Iterative Method (GTVIM) to solve the model, starting with specific initial conditions. This approach combines the

ρ

-Laplace Transform and the Variational Iterative Method. The Banach space fixed point theorem establishes the model’s existence and uniqueness. Furthermore, numerical analyses are performed for various fractional orders of two parameters to explore the dynamics of the rotavirus epidemic model.

轮状病毒感染是导致婴幼儿严重腹泻的一个重要原因，在全球范围内大大提高了死亡率。本研究探讨了不确定条件下轮状病毒的时间分数阶流行病模型，该模型使用卡图甘波拉分数导数（KFD）定义。我们采用一种称为广义变换变分迭代法（GTVIM）的半解析技术，从特定的初始条件开始求解该模型。这种方法结合了ρ-拉普拉斯变换和变分迭代法。巴拿赫空间定点定理确定了模型的存在性和唯一性。此外，还对两个参数的各种分数阶数进行了数值分析，以探索轮状病毒流行模型的动态。

引用次数: 0

Lie group classification and conservation laws of a (2+1)-dimensional nonlinear damped Klein–Gordon Fock equation (2+1)- 维非线性阻尼克莱因-戈登 Fock 方程的李群分类和守恒定律

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2024-10-18 DOI: 10.1016/j.padiff.2024.100962

Faiza Arif , Adil Jhangeer , F.M. Mahomed , F.D. Zaman

In this article, the

(2 + 1)

-dimensional nonlinear damped Klein–Gordon Fock equation is studied using the classical Lie symmetry method. A complete Lie group classification is conducted to derive the specific forms of the arbitrary smooth functions included in the equation, resulting in two distinct cases. Using the similarity transformation method, the reductions of the considered equation in the form of ordinary differential equations are obtained. Several invariant solutions including the traveling wave solutions and soliton solutions of the

(2 + 1)

-dimensional nonlinear damped Klein–Gordon Fock equation are uncovered. Also, the results are represented through 2D and 3D graphs with their physical interpretations. Notably, using the partial Lagrangian method, the conservation laws are derived, which also yield two separate cases with several subcases. These results offer better insights into the solution properties of nonlinear damped Klein–Gordon Fock equation and other complex nonlinear wave equations.

本文利用经典的李对称方法研究了 (2+1) 维非线性阻尼克莱因-戈登 Fock 方程。通过对方程中的任意光滑函数进行完整的李群分类，得出了两种不同的情况。利用相似变换法，得到了所考虑方程的常微分方程形式的还原。揭示了 (2+1)-dimensional 非线性阻尼克莱因-戈登 Fock 方程的若干不变解，包括行波解和孤子解。此外，这些结果还通过二维和三维图表示出来，并给出了物理解释。值得注意的是，利用部分拉格朗日方法推导出的守恒定律还产生了两个独立的情况，其中包括多个子情况。这些结果为非线性阻尼克莱因-戈登-福克方程和其他复杂非线性波方程的求解特性提供了更好的见解。

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引用次数: 0

Two-dimensional nonlinear Brinkman and steady-state Navier–Stokes equations for fluid flow in PCL PCL 中流体流动的二维非线性布林克曼方程和稳态纳维-斯托克斯方程

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2024-10-18 DOI: 10.1016/j.padiff.2024.100961

Surachai Phaenchat, Kanognudge Wuttanachamsri

To remove mucus from the human body, periciliary layer (PCL) is an important region found in the human respiratory system. When a human inhales strange particles along with air into the body, goblet cells inside the epithelial cells secrete mucus to catch those particles and form a mucus layer on the top of the PCL. Since the velocity of the fluid in the PCL and cilia residing in the PCL affect the movement of mucus, in this work, we apply two-dimensional nonlinear Brinkman and steady-state Navier–Stokes equations to find the velocity of the fluid in the PCL. In the equations, the velocity of cilia is also contributed in the mathematical model which perturbs the fluid movement instead of the pressure gradient. Because bundles of cilia are considered in this work rather than a single cilium, the governing equations are derived from the hybrid mixture theory (HMT) which are the equations in a macroscopic scale. The numerical solutions are obtained by using a mixed finite element method of Taylor–Hood type and Newton’s method. We focus on five different angles of cilia that make with the horizontal plane. The velocity of the PCL fluid is presented for each angle. The numerical solutions obtained in this study can be useful in finding the mucus velocity that can help physicians to treat patients who have massive mucus in their lungs.

为了清除人体内的粘液，纤毛层（PCL）是人体呼吸系统中的一个重要区域。当人将奇怪的微粒和空气一起吸入体内时，上皮细胞内的鹅口疮细胞会分泌粘液来捕捉这些微粒，并在 PCL 的顶部形成粘液层。由于 PCL 中流体的速度和驻留在 PCL 中的纤毛会影响粘液的运动，因此在本研究中，我们应用二维非线性布林克曼方程和稳态纳维-斯托克斯方程来计算 PCL 中流体的速度。在该方程中，纤毛的速度也被纳入数学模型，它代替压力梯度对流体运动产生扰动。由于本研究中考虑的是纤毛束而不是单根纤毛，因此控制方程是根据混合混合物理论（HMT）推导出来的，而混合混合物理论是宏观尺度上的方程。数值解法是通过泰勒胡德法和牛顿法的混合有限元法获得的。我们重点研究了纤毛与水平面的五个不同角度。每个角度下 PCL 流体的速度均有显示。本研究获得的数值解有助于找到粘液速度，从而帮助医生治疗肺部有大量粘液的患者。

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