Partial Differential Equations in Applied Mathematics最新文献

{"title":"Numerical simulation of multilane traffic flow model based on exponential velocity-density function","authors":"Md Rasel Ahmed ,&nbsp;Bitu Joydhar ,&nbsp;Dr. Md. Laek Sazzad Andallah ,&nbsp;Prokriti Biswas ,&nbsp;Jannatul Ferdous","doi":"10.1016/j.padiff.2025.101323","DOIUrl":"10.1016/j.padiff.2025.101323","url":null,"abstract":"<div><div>In this paper, we study a multilane traffic flow model incorporating the exponential velocity-density relationship, which yields a nonlinear first-order system of hyperbolic partial differential (PDEs) equations formulated as an initial-boundary value problem (IBVP). This study seeks to construct a physically consistent and computationally efficient model for a multilane traffic flow model, which captures nonlinear vehicular interactions and lane-changing dynamics. Numerical solutions of the multilane traffic flow model, under the specified initial and boundary conditions, are obtained using the finite difference method. The numerical simulations are performed by employing the well-known first-order Explicit Upwind Scheme, the Lax-Friedrichs Scheme, and the second-order Lax-Wendroff Scheme. We evaluate the convergence rate of the numerical solutions, along with detailed well-posedness and stability analysis. To assess the stability and accuracy of three numerical schemes, we compare the velocity and density profiles derived from different schemes. The outcomes of our study have significant applications in traffic management in the real world, including predicting the effect of congestion, optimizing the lane-change effects, and enhancing efficiency through intelligent transportation system intelligent transportation system (ITS) and safety on multilane highways.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"16 ","pages":"Article 101323"},"PeriodicalIF":0.0,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145576325","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On nonlinear ordinary differential system for infectious disease: A neuro-swarming intelligence scheme","authors":"Farhad Muhammad Riaz ,&nbsp;Junaid Ali Khan ,&nbsp;Khalil Ur Rehman ,&nbsp;Wasfi Shatanawi","doi":"10.1016/j.padiff.2025.101317","DOIUrl":"10.1016/j.padiff.2025.101317","url":null,"abstract":"<div><div>It is believed that nonlinear ordinary differential systems are essential for epidemic modeling because they can narrate the complex and unpredictable aspects of the spread of infectious diseases. Therefore, one can use nonlinear differential systems to propose control measures for the spread of diseases, and it remains a challenging task for researchers to obtain the best solution for such nonlinear systems. The present article offers the best solution remedy for nonlinear differential systems. To be more specific, to address the nonlinear dynamics of the spread of COVID-19, we propose an intelligent computational framework based on single-layer feed-forward artificial neural networks (FF-ANNs) and the optimization techniques of global and local search approaches. The SEIR-NDC model is solved by using a global-local search strategy called PSO<img>NM, which combines Particle Swarm Optimization (PSO) and the Nelder-Mead Simplex (NM). The differential nonlinear mathematical model based on SEIR-NDC and initial conditions is used in the hybrid PSO<img>NM combination to optimize an error-based fitness function. Ten neurons are used to demonstrate the numerical performance of the SEIR-NDC nonlinear model using ANN methods in conjunction with PSO-SQP. The correctness of the developed scheme is testified through the comparative analysis of the reference solution and the obtained outcomes. The absolute error performances are reported within appropriate ranges for every class of the SEIR-NDC model. It is found that the AE lies in the range 10^–14 and 10^–17. The statistical analysis is presented to verify the developed scheme's stability, convergence, and robustness. The statistical measures, i.e., mean square error falls between 10^–8 and 10^–13, while the mean absolute deviation falls between 10^–8 and 10^–11. We believe that the outcomes of the present analysis will be a helping hand in encountering nonlinear differential systems that are subject to practical applications.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"16 ","pages":"Article 101317"},"PeriodicalIF":0.0,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145417311","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Analytic investigation of the (2+1)-dimensional Heisenberg ferromagnetic spin chain equation with M-fractional derivative","authors":"Zehra Tat,&nbsp;Emrullah Yaşar","doi":"10.1016/j.padiff.2025.101302","DOIUrl":"10.1016/j.padiff.2025.101302","url":null,"abstract":"<div><div>In this study, we examine the Heisenberg ferromagnetic spin chain equation in complex form in (2+1) dimensions, which is closely related to ferromagnetic materials and is used in spin wave dynamics modeling. To better interpret the model physically, we considered M-truncated time fractional derivative operator and used the generalized exponential rational function and extended trial equation methods to reveal the exact solution forms. These exact solution forms are presented in hyperbolic, trigonometric, and rational forms. We give 2D and 3D numerical simulations of exact solution profiles. The importance of fractional calculus in extending nonlinear theory is emphasized.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"16 ","pages":"Article 101302"},"PeriodicalIF":0.0,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145221911","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Numerical solution of the variable-order time fractional advection reaction–diffusion equation via combination of a Newton’s polynomial and Cubic B-spline method","authors":"A.S.V. Ravi Kanth,&nbsp;Varela Pavankalyan","doi":"10.1016/j.padiff.2025.101289","DOIUrl":"10.1016/j.padiff.2025.101289","url":null,"abstract":"<div><div>This work presents a numerical technique based on the cubic B-spline function for solving the variable-order time fractional advection reaction–diffusion equation in the sense of the Caputo derivative. Newton’s interpolation formulation has been employed to approximate the variable-order time-fractional derivative, while the cubic B-spline functions are utilized for spatial discretization. The proposed methodology demonstrated unconditionally stable and convergence of order <span><math><mrow><mo>(</mo><mi>Δ</mi><msup><mrow><mstyle><mi>r</mi></mstyle></mrow><mrow><mn>4</mn><mo>−</mo><mi>ϑ</mi><mrow><mo>(</mo><mi>ς</mi><mo>,</mo><mstyle><mi>r</mi></mstyle><mo>)</mo></mrow></mrow></msup><mo>+</mo><msup><mrow><mi>h</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow></math></span> through the Von Neumann analysis. Numerical investigations that confirm theoretical conclusions using data visualizations and tables to illustrate efficiency and accuracy. Furthermore, the comparative findings demonstrate that the novel discretization methodology outperforms the other techniques present in the literature in terms of accuracy.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"16 ","pages":"Article 101289"},"PeriodicalIF":0.0,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145048528","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Hemodynamic analysis of Jeffrey blood flow with two-layered model through a multiple stenoses in a diverging narrow channel with a porous layer under slip conditions","authors":"K. Rajyalakshmi,&nbsp;G. Ravi Kiran,&nbsp;N. Lavanya","doi":"10.1016/j.padiff.2025.101307","DOIUrl":"10.1016/j.padiff.2025.101307","url":null,"abstract":"<div><div>This study provides an analytical examination of the hemodynamic characteristics of two-layered blood flow in a diverging narrow channel featuring multiple symmetrical stenoses, porous wall effects, and slip boundary conditions. The central region, characterized by a concentration of RBCs, is modeled as a Jeffrey fluid, whereas the peripheral region is considered Newtonian. Under the assumption of mild stenosis and incompressible, completely developed laminar movement, the governing equations are precisely formulated and solved through direct integration. Closed-form expressions for velocity, mean hematocrit, core hematocrit and effective viscosity have been obtained. Parametric analysis indicates that velocity escalates with the Jeffrey parameter and slip, whereas effective viscosity diminishes with elevated Jeffrey parameter and Darcy number values, but augments with slip and stenosis height. The core and mean hematocrit diminish with most parameter variations, yet increase with the Jeffrey parameter. These findings improve comprehension of pathological conditions such as arterial occlusions and illustrate microcirculatory effects, including the Fåhraeus–Lindqvist phenomenon. The integrated modeling framework enhances physiological relevance and facilitates biomedical applications in the diagnosis and treatment of vascular diseases.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"16 ","pages":"Article 101307"},"PeriodicalIF":0.0,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145268619","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Numerical study for inelastic fluid flow in a contraction-expansion axisymmetric channel by using the finite element method","authors":"Alaa A. Sharhan ,&nbsp;Adnan K. Farhood ,&nbsp;Alaa H. Al-Muslimawi","doi":"10.1016/j.padiff.2025.101311","DOIUrl":"10.1016/j.padiff.2025.101311","url":null,"abstract":"<div><div>This research looks at the flow of inelastic fluids in an axisymmetric 4:1:4 contraction-expansion with a sharp corner. The finite element approach is used to simulate the flow of inelastic fluid numerically. The continuity equation and the conversation equation of momentum equation are used in combination with the power law model. This study presents the extent of the influence of many factors, including the Reynolds number (Re) and the power law index <span><math><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow></math></span>, on the solution behavior. Our focus in this work is specifically on how these parameters effect the component of the solution and the convergence rate. The values of pressure and velocity were on of the interests of our research paper, as was the extent to which these are effected by the power law index and the Reynolds number. The influence of index <span><math><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow></math></span> of power law model on viscosity was also one of the subjects of the investigation.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"16 ","pages":"Article 101311"},"PeriodicalIF":0.0,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145466072","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Exploring solitary wave structures and bifurcation dynamics in the (2+1)-dimensional generalized Hietarinta equation","authors":"Yeşim Sağlam Özkan ,&nbsp;Esra Ünal Yılmaz","doi":"10.1016/j.padiff.2025.101283","DOIUrl":"10.1016/j.padiff.2025.101283","url":null,"abstract":"<div><div>This study investigates the <span><math><mrow><mo>(</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math></span>-dimensional generalized Hietarinta equation, which models the propagation of waves on water surfaces in the presence of gravity and surface tension. Solitary wave solutions are obtained using the <span><math><mrow><mi>e</mi><mi>x</mi><mi>p</mi><mrow><mo>(</mo><mo>−</mo><mi>w</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>)</mo></mrow></mrow></math></span> method and the <span><math><mi>F</mi></math></span>-expansion method, and are expressed in terms of hyperbolic, trigonometric, exponential and rational functions. Two- and three-dimensional plots illustrate various wave structures, such as dark, kinked, and singular kinked waves, highlighting their dynamic behaviors under different parameter settings. Hamiltonian functions and bifurcation theory are employed to analyze phase portraits and nonlinear wave dynamics, including chaotic behavior. Numerical simulations has been conducted using Mathematica and Maple confirm the theoretical findings. Additionally, the results have been compared with other existing results in the literature to show their uniqueness. The proposed techniques are effective, computationally efficient and reliable. In this context, considering previous studies, the findings of this research contribute to the existing literature.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"16 ","pages":"Article 101283"},"PeriodicalIF":0.0,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145044691","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dynamical wave structures for time-fractional (3+1)-dimensional p-type model via two improved techniques","authors":"Makhdoom Ali ,&nbsp;Muhammad Bilal Riaz ,&nbsp;Nauman Ahmed ,&nbsp;Muhammad Zafarullah Baber ,&nbsp;Ali Akgül","doi":"10.1016/j.padiff.2025.101303","DOIUrl":"10.1016/j.padiff.2025.101303","url":null,"abstract":"<div><div>In this work, we investigates the conformable time-fractional (3+1)-dimensional p-type model for the analytical solutions. The underlying model is explained the material characteristics and spontaneous processes in solid-state physics, such as magnetism and conventional particle physics. To obtain the analytical solutions, we used the novel Kumar–Malik method and the new extended direct algebraic method. We derived the analytical solutions through the application of the conformal fractional derivative and the fractional wave transformation. We successfully obtain several solutions in the form of rational, hyperbolic, mixed trigonometric, mixed hyperbolic, exponential, Jacobi elliptic, and trigonometric functions by using these methods. The found solutions include various solitary wave solutions as well as bright, dark, and w-shaped soliton solutions. With the use of Mathematica 13.0, the analytical soliton solutions are further shown in 3D, contour and 2D representations, assisting in the understanding of these complex wave phenomena.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"16 ","pages":"Article 101303"},"PeriodicalIF":0.0,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145221967","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Pseudo-planar deformations of a linearized elastic solid","authors":"E. Momoniat ,&nbsp;C. Harley","doi":"10.1016/j.padiff.2025.101301","DOIUrl":"10.1016/j.padiff.2025.101301","url":null,"abstract":"<div><div>The equations of motion for the pseudo-planar motions of a classical linearized elastic solid and an incompressible linearized elastic solid undergoing non-uniform rotation about a vertical axis are derived. The pseudo-planar motions for both a classical linearized and an incompressible linearized elastic solid are determined numerically. For a classical linearized elastic solid, the non-uniform rotation is time-dependent and is specified. We derive a wave equation that models the non-uniform rotation for an incompressible linearized elastic solid. A pressure Poisson equation is derived and depends on the time derivative of the non-uniform rotation. The locus of the equations of motion coupled with the pseudo-planar motions of a cylindrical solid are plotted and the results are discussed. We show that the pseudo-planar motions of a classical linearized elastic solid with zero rotation are translations of the pseudo-planes about the locus. The pseudo-plane motions for classical and incompressible linearized elastic solids undergo translations and rotations about the locus. The motions are bound and stable when the pressure is symmetric. Unsymmetric pressure, which is just the mechanical pressure, results in a distortion of the pseudo-planar curves.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"16 ","pages":"Article 101301"},"PeriodicalIF":0.0,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145107802","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Optimal design problem with thermal radiation","authors":"Kosuke Kita ,&nbsp;Kei Matsushima ,&nbsp;Tomoyuki Oka","doi":"10.1016/j.padiff.2025.101304","DOIUrl":"10.1016/j.padiff.2025.101304","url":null,"abstract":"<div><div>This paper is concerned with configurations of two-material thermal conductors that minimize the Dirichlet energy for steady-state diffusion equations with nonlinear boundary conditions described mainly by maximal monotone operators. To find such configurations, a homogenization theorem will be proved and applied to an existence theorem for minimizers of a relaxation problem whose minimum value is equivalent to an original design problem. As a typical example of nonlinear boundary conditions, thermal radiation boundary conditions will be the focus, and then the sensitivity of the Dirichlet energy will be derived, which is used to estimate the minimum value. Since optimal configurations of the relaxation problem involve the so-called grayscale domains that do not make sense in general, a perimeter constraint problem via the positive part of the level set function will be introduced as an approximation problem to avoid such domains, and moreover, the existence theorem for minimizers of the perimeter constraint problem will be proved. In particular, it will also be proved that the limit of minimizers for the approximation problem becomes that of the relaxation problem in a specific case, and then candidates for minimizers of the approximation problem will be constructed by employing a nonlinear diffusion-based level set method. In this paper, it will be shown that optimized configurations deeply depend on force terms as a characteristic of nonlinear problems and will also be applied to real physical problems.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"16 ","pages":"Article 101304"},"PeriodicalIF":0.0,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145362460","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}