Partial Differential Equations in Applied Mathematics最新文献

{"title":"Approximate analytical solution of a class of highly nonlinear time–fractional-order partial differential equations","authors":"Richard Olu Awonusika","doi":"10.1016/j.padiff.2025.101090","DOIUrl":"10.1016/j.padiff.2025.101090","url":null,"abstract":"<div><div>This article presents a power series technique for obtaining approximate solutions of the time–fractional-order version of a generalised Newell–Whitehead–Segel initial value problem, with the fractional-order derivative described in the Caputo sense. The method assumes a fractional power series in the time variable whose expansion coefficients are functions of the space variable. The proposed approach is based on the generalised Cauchy product of power series and does not require any kind of polynomial or digitisation in the simplification of the nonlinear terms. The application of the generalised Cauchy product enables us to construct explicit recursion formulae for the expansion coefficients of the series solution. The first expansion coefficients are nicely expressed in terms of appropriate integer sequences. Notable special cases of the proposed generalised problem, that include, Newell-Whitehead, Newell–Whitehead–Segel, and Cahn–Allen equations with suitable initial conditions are considered for the purpose of accuracy and reliability of the proposed method. Our numerical results are compared with the exact solutions and other existing results. Comparison of the absolute errors from our method and other published results indicates that the proposed technique is accurate and reliable. Two-dimensional and three-dimensional graphs of results are presented for different fractional-order values <span><math><mrow><mn>0</mn><mo>&lt;</mo><mi>μ</mi><mo>≤</mo><mn>1</mn></mrow></math></span>. It is observed that as the fractional-order <span><math><mi>μ</mi></math></span> gets closer to 1, the graphs of the approximate solutions gradually coincide with those of the exact solutions. The convergence rate of the proposed series solutions ranges between <span><math><mrow><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>15</mn></mrow></msup></mrow></math></span> and <span><math><mrow><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>18</mn></mrow></msup></mrow></math></span>.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101090"},"PeriodicalIF":0.0,"publicationDate":"2025-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163833","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}

{"title":"On the novel nonlinear propagating waves in stochastic dispersive mode","authors":"H.G. Abdelwahed ,&nbsp;A.F. Alsarhan ,&nbsp;E.K. El-Shewy ,&nbsp;Mahmoud A.E. Abdelrahman","doi":"10.1016/j.padiff.2025.101089","DOIUrl":"10.1016/j.padiff.2025.101089","url":null,"abstract":"<div><div>The solutions of the nonlinear Schrödinger equations (NLSEs) predict the presence of consistent, novel and applicable existences including solitonic localized structures, rouge forms and shocks that propagate based on of physical parameters. The NLSEs with stochastic characteristics predict the anticipated nonlinear process generating decay or forcing in various wave applications. In this work, we discuss the NLSE via noise in Itô sense. New soliton-like, periodic waves and shocks solutions are presented in this study. The presented stochastic structures become crucial in the restricted relationship between the model’s nonlinearity, dispersion, and dissipative impacts. These stochastic structures generated changes in frequencies and density structures via noise term. It was observed that noise effects might alter the wave characteristics, thereby producing unprecedented physical and astrophysical densities.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101089"},"PeriodicalIF":0.0,"publicationDate":"2025-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143165070","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}

{"title":"A simple model of the Draupner Wave Experiment","authors":"Graeme Hocking ,&nbsp;Emma Nel ,&nbsp;Alice Markham ,&nbsp;Erick Mubai ,&nbsp;Thama Duba ,&nbsp;Samah Ali ,&nbsp;Hloniphile Sithole Mthethwa ,&nbsp;Morwakoma Matabane ,&nbsp;Ndivhuwo Ndou ,&nbsp;Katlego Sebogodi ,&nbsp;Salma Ahmedai ,&nbsp;Nyathi Freeman","doi":"10.1016/j.padiff.2025.101085","DOIUrl":"10.1016/j.padiff.2025.101085","url":null,"abstract":"<div><div>Rogue Waves are large waves that appear “out of nowhere” in the open ocean and in near-shore waters. The Mathematics in Industry Study Group organized by Professor David Mason at the University of Witwatersrand in January, 2024, considered these waves due to their frequency at locations off the South African coast. There are a number of quite sophisticated models of these waves, but in this work we try to reproduce something like a rogue wave with a very simple free surface model, and in particular consider a wave generated in a circular tank by wave activity at the outer edge. Linear and nonlinear equations are derived and integrated to obtain the wave activity due to different generation mechanisms. The results indicate that a relatively simple model can produce something that approaches the form of a rogue wave.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101085"},"PeriodicalIF":0.0,"publicationDate":"2025-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143165077","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}

{"title":"Analysis of water based Casson hybrid nanofluid (NiZnFe2O4+MnZnFe2O4) flow over an electromagnetic actuator with Cattaneo–Christov heat-mass flux: A modified Buongiorno model","authors":"S. Baskaran ,&nbsp;R. Sowrirajan ,&nbsp;S. Divya ,&nbsp;S. Eswaramoorthi ,&nbsp;K. Loganathan","doi":"10.1016/j.padiff.2025.101079","DOIUrl":"10.1016/j.padiff.2025.101079","url":null,"abstract":"<div><div>The Casson hybrid nanofluid has pivotal role in boosting heat transfer capableness in several industrial and technological applications. In light of this consideration, the current inquisition examined the Darcy–Forchheimer flow of a water-based mono nanofluid (<span><math><mrow><msub><mrow><mi>NiZnFe</mi></mrow><mrow><mn>2</mn></mrow></msub><msub><mrow><mi>O</mi></mrow><mrow><mn>4</mn></mrow></msub></mrow></math></span>) and hybrid nanofluid (<span><math><mrow><msub><mrow><mi>NiZnFe</mi></mrow><mrow><mn>2</mn></mrow></msub><msub><mrow><mi>O</mi></mrow><mrow><mn>4</mn></mrow></msub><mo>+</mo><msub><mrow><mi>MnZnFe</mi></mrow><mrow><mn>2</mn></mrow></msub><msub><mrow><mi>O</mi></mrow><mrow><mn>4</mn></mrow></msub></mrow></math></span>) past a stretched Riga plate with Cattaneo–Christov heat-mass flux and nonlinear radiation. Additionally, this inspection focuses on analyzing the upshot of heat generation/absorption, Brownian motion, thermophoresis, and Lewis number. Using suitable variables, the governing coupled nonlinear partial differential equations are transformed into ordinary differential equations, which are solved using MATLABs bvp4c solver. The implication of key parameters on both direction velocities, temperature, nanofluid concentration, skin friction coefficients, local Nusselt number, and Sherwood number are displayed graphically. Our investigation revealed that fluid velocities are suppressed by increasing the values of Forchheimer number. The temperature profile grows when magnifying the values of Brownian motion and thermophoresis parameters. The Lewis number and mass relaxation time parameter declines the nanofluid concentration profile. The surface shear stress slumps when upgrades the Casson parameter and porosity parameter. The heat transfer rate enriches when elevating the quantities of radiation parameter and Biot number. Brownian motion and thermophoresis parameters reduce the mass transfer rate.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101079"},"PeriodicalIF":0.0,"publicationDate":"2025-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163922","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}

{"title":"Conformable variational iteration method for solving fuzzy variable-order fractional partial differential equations with proportional delay","authors":"Abbas I. Khlaif ,&nbsp;Osama H. Mohammed ,&nbsp;Moez Feki","doi":"10.1016/j.padiff.2024.101064","DOIUrl":"10.1016/j.padiff.2024.101064","url":null,"abstract":"<div><div>In this study, we use the conformable variational iteration method for solving delay fuzzy variable-order fractional partial differential equations. The fractional order derivative will be taken to be of conformable type. The proposed method provides a sequence of functions which is convergent to the exact solution. We emphasize the power of the method by testing some examples. The conformable variational iteration method, has proven to be highly accurate and dependable in solving non-linear delay fuzzy variable-order fractional partial differential equations.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101064"},"PeriodicalIF":0.0,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143165069","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}

{"title":"Mathematical modelling of flow and adsorption in a gas chromatograph","authors":"A. Cabrera-Codony ,&nbsp;A. Valverde ,&nbsp;K. Born ,&nbsp;O.A.I. Noreldin ,&nbsp;T.G. Myers","doi":"10.1016/j.padiff.2025.101074","DOIUrl":"10.1016/j.padiff.2025.101074","url":null,"abstract":"<div><div>In this paper, a mathematical model is developed to describe the evolution of the concentration of compounds through a gas chromatography column. The model couples mass balances and kinetic equations for all components. Both single and multiple-component cases are considered with constant or variable velocity. Dimensional analysis is employed to identify negligible terms and so reduce the problem to the solution of a single integral equation. From this the concentration profile for all components may be determined (since they are scaled versions of each other). The full governing equations are also solved numerically to verify the analytical approach. Finally the analytical results are compared with experimental data, showing excellent agreement. This novel method is highly efficient and is significantly faster and simpler than previous numerical approaches.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101074"},"PeriodicalIF":0.0,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163400","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}

{"title":"Finite volume modeling of neural communication: Exploring electrical signaling in biological systems","authors":"Muzammal Saleem ,&nbsp;Muhammad Saqib ,&nbsp;Badar Saad Alshammari ,&nbsp;Shahid Hasnain ,&nbsp;Amjad Ayesha","doi":"10.1016/j.padiff.2025.101082","DOIUrl":"10.1016/j.padiff.2025.101082","url":null,"abstract":"<div><div>This article investigates neuronal dynamics in neuroscience, employing mathematical frameworks such as the Hodgkin Huxley model to describe them. Action potentials electrical signals generated by neurons are crucial for communication within the nervous system. The Hodgkin–Huxley model offers an analytically representation of how neurons produce and propagate these action potentials by accounting for key factors, including membrane potential variations influenced by ion channel conductances. These ion channels regulate ion movement across cell membranes, which is essential for neuronal activity. The model has been widely applied to study phenomena such as neural network behavior and the impact of drugs on neuronal function. The proposed numerical approach, based on a hyperbolic tangent (tanh) function, is shown to be second-order accurate and unconditionally stable. Validation through comparison with existing literature and computational simulations demonstrates strong agreement between predicted outcomes and those generated by the model. The numerical method proves to be a reliable and precise tool for modeling the dynamics of physical systems, with potential applications in fields such as electromagnetism, acoustics, and fluid mechanics.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101082"},"PeriodicalIF":0.0,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163942","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}

{"title":"Dynamical analysis of a complex competitive two-strain epidemic network model with vaccination","authors":"A. Abdelkhalek ,&nbsp;A.H. Abdel Kader ,&nbsp;I.L. El-Kalla ,&nbsp;A. Elsaid ,&nbsp;Amr Elsonbaty ,&nbsp;K.S. Nisar","doi":"10.1016/j.padiff.2024.101058","DOIUrl":"10.1016/j.padiff.2024.101058","url":null,"abstract":"<div><div>Developing accurate models to replicate epidemic transmission poses a significant challenge for researchers both now and in the foreseeable future. Therefore, this work proposes a new complex competitive two-strain epidemic network model that incorporates vaccination. We derive the mathematical model, compute the disease-free equilibrium point, and determine its stability conditions. The basic reproduction number is computed to determine the epidemic threshold. The stability regions in parameter space and the effects of vaccination parameters are obtained. The conditions for transcritical bifurcation are established, and the parameter analysis for this type of bifurcation is conducted. Numerical simulations of various scenarios with varying parameter values validate the theoretical analysis.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101058"},"PeriodicalIF":0.0,"publicationDate":"2025-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163943","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}

{"title":"MHD flow of Williamson nanofluid using effective similarity variable considering viscous dissipation and thermal radiation over a non-linear stretching surface via OHAM","authors":"Muhammad Awais Sherani ,&nbsp;Muhammad Sohail ,&nbsp;Ibrahim Mahariq ,&nbsp;Syed Tehseen Abbas","doi":"10.1016/j.padiff.2025.101088","DOIUrl":"10.1016/j.padiff.2025.101088","url":null,"abstract":"<div><div>This work examines the 2D surface layer flow of Williamson Nano fluid across a non-linear extendable sheet utilizing magneto hydrodynamics (MHD), taking into account the impacts of heat generation(<em>S</em>), thermal radiation(<em>Rd</em>), chemical reaction(<em>Cr</em>), and viscous dissipation. This evaluation goes beyond the localized impacts usually taken into account in each linear and non-linear stretching scenario, and instead focuses on global impact of the not Newtonian Williamson fluid factor. The conservation laws of mass, momentum, and energy which are represented as partial differential equations form the foundation of the mathematical model. Using an appropriate similarity transformation, these equations are converted into ordinary differential equations, which can then be resolved numerically OHAM technique. The results depict the scenario in which with increasing values of <em>λ</em> and <em>M</em>, the velocity reduces because resistance is increased; meanwhile, the temperature profile is inversely proportional to higher <em>Pr, Le</em>, and <em>Nbt</em>, where it decreases because thermal diffusivity diminishes. Conversely, with an increase in <em>Rd, Nc</em>, and <em>S</em>, the thermal profiles augment. Concentration diminishes with the augmentation of <em>Sc, Cr</em>, and <em>Nbt</em> due to intensified Brownian motion and molecular interactions. It is observed that λ and <em>M</em> increase the value of skin friction, but −θ'(0), indicating heat transfer efficiency, increases with <em>Pr, Le</em>, and <em>Nbt</em> but declines with Rd and <em>Nc</em>. The mass transfer rate of −g'(0) is found to rise positively with <em>Sc, Cr</em>, and <em>Nbt</em>, which indicates an interacting relationship between the temperature and concentration fields in the fluid system.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101088"},"PeriodicalIF":0.0,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163941","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}

{"title":"Overtaking solitary wave collisions for Whitham–Boussinesq systems","authors":"Marcelo V. Flamarion ,&nbsp;Rosa Maria Vargas-Magaña","doi":"10.1016/j.padiff.2025.101080","DOIUrl":"10.1016/j.padiff.2025.101080","url":null,"abstract":"<div><div>This study focuses on solitary waves and their pairwise interactions within two fully dispersive and weakly nonlinear models known as Whitham–Boussinesq systems. Solitary waves are numerically computed using an iterative Newton-type method, incorporating continuation in wave amplitude and speed. These computed solitary waves are then used as initial data to study overtaking collisions in both systems. Our findings show that both systems satisfy the geometric Lax-categorisation for two-soliton collisions. Additionally, numerical evidence suggests that one of the systems admits an algebraic Lax-categorisation, though within a different range than that originally demonstrated by Lax for the Korteweg–de Vries equation. However, this algebraic categorisation does not apply for the second system. Additionally, qualitative and numerical analyses of solitary waves governed by each Whitham–Boussinesq system, including their amplitude-velocity relations, are presented and compared using two independent approaches.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101080"},"PeriodicalIF":0.0,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143165068","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}