Pub Date : 2025-09-01DOI: 10.1016/j.padiff.2025.101286
Nauman Ahmed , Sidra Ghazanfar , Zunaira , Muhammad Z. Baber , Ilyas Khan , Osama Oqilat , Wei Sin Kohh
This work suggests single-wave solutions for the Estevez-Mansfield-Clarkson (EMC) and linked sine-Gordon equations. The shape generation process in droplet form is studied using these model equations. For accurate wave and solitary wave solutions, in addition to many mathematical and physical research methods. There is nonlinear dispersion according to the EMC equation. It is feasible to generalize the Estevez-Mansfield integrable. Precise wave solutions, including kink, solitary, rational, single, and anti-kink, may be obtained by modifying the generalized exponential rational function technique. These changes may be advantageous in several scientific and technological domains. A novel approach to the precise solution of nonlinear partial differential equations is presented in this paper. The strategy’s main objective is to increase the applicability of the exponential rational function technique.
{"title":"Campatibility of solitons within the frame work of Estevez-Mansfield-Clarkson equation","authors":"Nauman Ahmed , Sidra Ghazanfar , Zunaira , Muhammad Z. Baber , Ilyas Khan , Osama Oqilat , Wei Sin Kohh","doi":"10.1016/j.padiff.2025.101286","DOIUrl":"10.1016/j.padiff.2025.101286","url":null,"abstract":"<div><div>This work suggests single-wave solutions for the Estevez-Mansfield-Clarkson (EMC) and linked sine-Gordon equations. The shape generation process in droplet form is studied using these model equations. For accurate wave and solitary wave solutions, in addition to many mathematical and physical research methods. There is nonlinear dispersion according to the EMC equation. It is feasible to generalize the Estevez-Mansfield integrable. Precise wave solutions, including kink, solitary, rational, single, and anti-kink, may be obtained by modifying the generalized exponential rational function technique. These changes may be advantageous in several scientific and technological domains. A novel approach to the precise solution of nonlinear partial differential equations is presented in this paper. The strategy’s main objective is to increase the applicability of the exponential rational function technique.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101286"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145018459","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}
Pub Date : 2025-09-01DOI: 10.1016/j.padiff.2025.101271
Alemu Senbeta Bekela , Mesfin Mekuria Woldaregay
Nonlinear time-fractional diffusion equations (NTFDEs) are widely applied for modeling various natural processes like volcanic eruption, diffusion processes, earthquakes, brain tumors, and the dynamics of soil in water. Solving these problems is quite challenging. So, designing effective numerical approaches is an active research area. The fractional derivative used is the Caputo type. In this paper, we develop the hybrid series based method by combining the Formable transform and Adomian decomposition method (ADM) for treating the NTFDEs. The stability and convergence of the developed series based method have been investigated. The effectiveness of the introduced method is investigated by solving two test examples. The obtained numerical results show that the proposed method is efficient for solving NTFDEs and gives accurate results.
{"title":"Formable transform Adomian decomposition method for solving nonlinear time-fractional diffusion equation","authors":"Alemu Senbeta Bekela , Mesfin Mekuria Woldaregay","doi":"10.1016/j.padiff.2025.101271","DOIUrl":"10.1016/j.padiff.2025.101271","url":null,"abstract":"<div><div>Nonlinear time-fractional diffusion equations (NTFDEs) are widely applied for modeling various natural processes like volcanic eruption, diffusion processes, earthquakes, brain tumors, and the dynamics of soil in water. Solving these problems is quite challenging. So, designing effective numerical approaches is an active research area. The fractional derivative used is the Caputo type. In this paper, we develop the hybrid series based method by combining the Formable transform and Adomian decomposition method (ADM) for treating the NTFDEs. The stability and convergence of the developed series based method have been investigated. The effectiveness of the introduced method is investigated by solving two test examples. The obtained numerical results show that the proposed method is efficient for solving NTFDEs and gives accurate results.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101271"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145018460","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}
Pub Date : 2025-09-01DOI: 10.1016/j.padiff.2025.101300
Attia Rani , Muhammad Shakeel , Muhammad Sohail , Ibrahim Mahariq
In this work, we examine the Heimburg model, which describes how electromechanical pulses are transmitted through nerves by using the generalizing Riccati equation mapping method. This approach is regarded as one of the most recent efficient analytical approaches for nonlinear evolution equations, yielding numerous different types of solutions for the model under consideration. We get novel analytic exact solitary wave solutions, including exponential, hyperbolic, and trigonometric functions. These solutions comprises solitary wave, kink, singular kink, periodic, singular soliton, combined dark bright soliton, and breather soliton. To understand the physical principles and significance of the technique the well-furnished results are ultimately displayed in a variety of 2D, 3D, and contour profiles. Additionally, a stability study of the derived solutions is conducted, demonstrating that the steady state is stable under specific parameter restrictions, however the breach of these requirements results in instability due to the exponential increase of perturbations. The results of this work shed light on the importance of studying various nonlinear wave phenomena in nonlinear optics and physics by showing how important it is to understand the behaviour and physical meaning of the studied model. The employed methodology possesses sufficient capability, efficacy, and brevity to enable further research.
{"title":"The generalizing riccati equation mapping method's application for detecting soliton solutions in biomembranes and nerves","authors":"Attia Rani , Muhammad Shakeel , Muhammad Sohail , Ibrahim Mahariq","doi":"10.1016/j.padiff.2025.101300","DOIUrl":"10.1016/j.padiff.2025.101300","url":null,"abstract":"<div><div>In this work, we examine the Heimburg model, which describes how electromechanical pulses are transmitted through nerves by using the generalizing Riccati equation mapping method. This approach is regarded as one of the most recent efficient analytical approaches for nonlinear evolution equations, yielding numerous different types of solutions for the model under consideration. We get novel analytic exact solitary wave solutions, including exponential, hyperbolic, and trigonometric functions. These solutions comprises solitary wave, kink, singular kink, periodic, singular soliton, combined dark bright soliton, and breather soliton. To understand the physical principles and significance of the technique the well-furnished results are ultimately displayed in a variety of 2D, 3D, and contour profiles. Additionally, a stability study of the derived solutions is conducted, demonstrating that the steady state is stable under specific parameter restrictions, however the breach of these requirements results in instability due to the exponential increase of perturbations. The results of this work shed light on the importance of studying various nonlinear wave phenomena in nonlinear optics and physics by showing how important it is to understand the behaviour and physical meaning of the studied model. The employed methodology possesses sufficient capability, efficacy, and brevity to enable further research.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101300"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145018632","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}
Pub Date : 2025-09-01DOI: 10.1016/j.padiff.2025.101288
Sajid Shafique , Muhammad Afzal , Muhammad Arsalan Ahmad , Mohammad Mahtab Alam
Parametric analysis of different choices of acoustic absorbent liners in a bicameral acoustic duct is presented in the current research study. Bicameral is characterized by two expansion chambers but functions as a single duct in practice, that is widely used in various engineering applications, particularly in the field of exhaust systems and to mitigate noise. The current research intends to examine the acoustic behavior in an acoustic duct when it is equipped with fibrous and perforated liners in bicameral configurations. The comparison study of rigid vertical walls of the bicameral with absorbent liner materials is addressed particularly to optimize the design of an acoustic duct to accomplish the desired acoustic performance. The current physical challenge is modeled mathematically and solved by a semi-analytical Mode-Matching (MM) approach. However, the root findings of the derived dispersion relations and recasting the system of linear algebraic equations are tackled numerically. The power fluxes, transmission-loss (TL), and absorption power () as a function of frequency and against horizontal spacing of the chambers (L) are achieved and displayed graphically. Also, the comparison discussion is provided for both vertical rigid and vertical lining cases by assuming the various choices of fibrous absorbent liner (FAL) and perforated absorbent liner (PAL). Ahead of this, the computational validation of the analytical perspective also depends on satisfying matching continuity criteria.
{"title":"Parametric analysis of acoustic liner in bicameral duct: An analytical perspective","authors":"Sajid Shafique , Muhammad Afzal , Muhammad Arsalan Ahmad , Mohammad Mahtab Alam","doi":"10.1016/j.padiff.2025.101288","DOIUrl":"10.1016/j.padiff.2025.101288","url":null,"abstract":"<div><div>Parametric analysis of different choices of acoustic absorbent liners in a bicameral acoustic duct is presented in the current research study. Bicameral is characterized by two expansion chambers but functions as a single duct in practice, that is widely used in various engineering applications, particularly in the field of exhaust systems and to mitigate noise. The current research intends to examine the acoustic behavior in an acoustic duct when it is equipped with fibrous and perforated liners in bicameral configurations. The comparison study of rigid vertical walls of the bicameral with absorbent liner materials is addressed particularly to optimize the design of an acoustic duct to accomplish the desired acoustic performance. The current physical challenge is modeled mathematically and solved by a semi-analytical Mode-Matching (MM) approach. However, the root findings of the derived dispersion relations and recasting the system of linear algebraic equations are tackled numerically. The power fluxes, transmission-loss (TL), and absorption power (<span><math><msub><mrow><mi>P</mi></mrow><mrow><mi>a</mi><mi>b</mi><mi>s</mi></mrow></msub></math></span>) as a function of frequency and against horizontal spacing of the chambers (L) are achieved and displayed graphically. Also, the comparison discussion is provided for both vertical rigid and vertical lining cases by assuming the various choices of fibrous absorbent liner (FAL) and perforated absorbent liner (PAL). Ahead of this, the computational validation of the analytical perspective also depends on satisfying matching continuity criteria.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101288"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144923055","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}
Pub Date : 2025-08-27DOI: 10.1016/j.padiff.2025.101277
Salena Akther , M.G. Hafez , Shahrina Akter
The time–space fractional modified Korteweg de-Vries (TSF-mKdV) equation is considered to investigate the nonlinear overtaking ion-acoustic multi-solitons around the critical values of any specific physical parameter in an unmagnetized collisionless plasma. To do so, various fractional derivative operators are considered. The TSF-mKdV equation is actually obtained by applying the Agrawal technique to the typical mKdV equation. The Hirota’s direct bilinear approach is used to obtain the proposed multi-soliton solutions to the TSF-mKdV model equation. In the framework under study, the effects of the space–time fractional parameters and plasma parameters on the overtaking collision of multi-soliton wave propagation are examined.
{"title":"A comparative study on overtaking collisional ion-acoustic multi-soliton around the critical values in the sense of fractal and fractional differential operators","authors":"Salena Akther , M.G. Hafez , Shahrina Akter","doi":"10.1016/j.padiff.2025.101277","DOIUrl":"10.1016/j.padiff.2025.101277","url":null,"abstract":"<div><div>The time–space fractional modified Korteweg de-Vries (TSF-mKdV) equation is considered to investigate the nonlinear overtaking ion-acoustic multi-solitons around the critical values of any specific physical parameter in an unmagnetized collisionless plasma. To do so, various fractional derivative operators are considered. The TSF-mKdV equation is actually obtained by applying the Agrawal technique to the typical mKdV equation. The Hirota’s direct bilinear approach is used to obtain the proposed multi-soliton solutions to the TSF-mKdV model equation. In the framework under study, the effects of the space–time fractional parameters and plasma parameters on the overtaking collision of multi-soliton wave propagation are examined.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101277"},"PeriodicalIF":0.0,"publicationDate":"2025-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144914037","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}
Pub Date : 2025-08-27DOI: 10.1016/j.padiff.2025.101278
Ruchika Lochab , Luckshay Batra
The selection of suitable fuzzy logic control (FLC) systems for stabilizing hyperbolic conservation laws (HCLs) remains an open issue in computational fluid dynamics (CFD), particularly for shock-capturing schemes. This work addresses this gap by adopting a dual methodological strategy: (i) a systematic review of over 50 studies (2000–2025) on flux-limiting FLC approaches, and (ii) a comparative benchmark of Mamdani- and Sugeno-type FLCs applied to discontinuous solutions of HCLs. Our results demonstrate that, using weighted average defuzzification, Sugeno-type systems achieve approximately a 20% reduction in mean square error compared to the Mamdani centroid-based method in shock-dominated regimes. This performance gain aligns with adaptive CFD practices that prioritize rule-based, computationally inexpensive smoothing. By integrating theoretical analysis with experimental validation, this work strengthens the mathematical foundations of fuzzy control in PDE-driven modelling.
{"title":"Application of fuzzy logic controls on hyperbolic differential equations","authors":"Ruchika Lochab , Luckshay Batra","doi":"10.1016/j.padiff.2025.101278","DOIUrl":"10.1016/j.padiff.2025.101278","url":null,"abstract":"<div><div>The selection of suitable fuzzy logic control (FLC) systems for stabilizing hyperbolic conservation laws (HCLs) remains an open issue in computational fluid dynamics (CFD), particularly for shock-capturing schemes. This work addresses this gap by adopting a dual methodological strategy: (i) a systematic review of over 50 studies (2000–2025) on flux-limiting FLC approaches, and (ii) a comparative benchmark of Mamdani- and Sugeno-type FLCs applied to discontinuous solutions of HCLs. Our results demonstrate that, using weighted average defuzzification, Sugeno-type systems achieve approximately a 20% reduction in mean square error compared to the Mamdani centroid-based method in shock-dominated regimes. This performance gain aligns with adaptive CFD practices that prioritize rule-based, computationally inexpensive smoothing. By integrating theoretical analysis with experimental validation, this work strengthens the mathematical foundations of fuzzy control in PDE-driven modelling.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101278"},"PeriodicalIF":0.0,"publicationDate":"2025-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144914038","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}
Pub Date : 2025-08-26DOI: 10.1016/j.padiff.2025.101297
Rezaul Karim , M. A. Bkar Pk , M. Ali Akbar , Pinakee Dey
Leukemia is the name for a blood cancer that develops in the bone marrow. Leukemia is a global public health issue caused by the uncontrolled growth of immature white blood cells in the bloodstream. In this study, we consider a fractional-order five-compartment mathematical model (MM) of leukemia, which includes susceptible blood cells, infected blood cells , cancer cells , immune blood cells , cytokine cells , and we analyze the dynamics of transmission of the disease. We developed a model to examine the spread of the leukemia virus and analyze the effects of adoptive T-cell therapy. This study presents a model of the well-known leukemia virus utilizing Caputo fractional order (CFO) and Beta derivatives. In this, the extended system characterizing the virus spread is addressed using two analytical methods: the Laplace perturbation method (LPM) and the Homotopy decomposition method (HDM). Iterative schemes were employed to obtain specific solutions of the extended system, and numerical simulations were conducted based on selected theoretical parameters. Moreover, the concerned analytical solutions that have been found using the methods are compared. The corresponding plots against various orders of the differentiations are plotted using specific values for the model’s parameters. We emphasize the significance of fractional-order (FO) modeling in understanding the spread of leukemia and highlight the critical need for global access to this immunotherapy.
{"title":"A study on fractional-order mathematical analysis for inspecting the spread of the leukemia virus","authors":"Rezaul Karim , M. A. Bkar Pk , M. Ali Akbar , Pinakee Dey","doi":"10.1016/j.padiff.2025.101297","DOIUrl":"10.1016/j.padiff.2025.101297","url":null,"abstract":"<div><div>Leukemia is the name for a blood cancer that develops in the bone marrow. Leukemia is a global public health issue caused by the uncontrolled growth of immature white blood cells in the bloodstream. In this study, we consider a fractional-order five-compartment mathematical model (MM) of leukemia, which includes susceptible blood cells<span><math><mrow><mspace></mspace><msub><mi>S</mi><mn>1</mn></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span>, infected blood cells <span><math><mrow><msub><mi>I</mi><mn>1</mn></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span>, cancer cells <span><math><mrow><msub><mi>C</mi><mn>1</mn></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span>, immune blood cells <span><math><mrow><msub><mi>W</mi><mn>1</mn></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span>, cytokine cells <span><math><mrow><msub><mi>C</mi><mn>2</mn></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span>, and we analyze the dynamics of transmission of the disease. We developed a model to examine the spread of the leukemia virus and analyze the effects of adoptive T-cell therapy. This study presents a model of the well-known leukemia virus utilizing Caputo fractional order (CFO) and Beta derivatives. In this, the extended system characterizing the virus spread is addressed using two analytical methods: the Laplace perturbation method (LPM) and the Homotopy decomposition method (HDM). Iterative schemes were employed to obtain specific solutions of the extended system, and numerical simulations were conducted based on selected theoretical parameters. Moreover, the concerned analytical solutions that have been found using the methods are compared. The corresponding plots against various orders of the differentiations are plotted using specific values for the model’s parameters. We emphasize the significance of fractional-order (FO) modeling in understanding the spread of leukemia and highlight the critical need for global access to this immunotherapy.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101297"},"PeriodicalIF":0.0,"publicationDate":"2025-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144914036","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}
Pub Date : 2025-08-23DOI: 10.1016/j.padiff.2025.101294
Shilpa Choudhary , Ruchika Mehta , Tripti Mehta
This research presents a comparative analysis of Cross diffusion effect on 2D MHD chemical reactive Williamson hybrid nanofluid (MoS2 − GO/Methanol) on a moving thin needle with thermal radiation. The main aim of this study is to increase the thermal efficiency using two different categories of nanoparticles: MoS2 − GO, with Methanol serving as the original liquid is calculated. PDEs can be changed into ordinary differential equations with the help of similarity substitution. Which are nonlinear, and the bvp4c technique is used to numerically simplify it. The results of this investigation indicate that the velocity profile of GO/Methanol composite nanofluid increases more than that of MoS2 − GO/Methanol through the increasing amount of Grashof number and Weissenberg parameter, even as the magnetic parameter and porosity impact have the opposite effect. On other hand, the chemical reaction and Schmidt number increase the rate of mass transfer for both nanofluids. The larger values of thermal radiation and Dufour effect enhance the thermal profile.
{"title":"Numerical study of MHD Williamson hybrid nanofluid flow over incessantly moving thin needle in presence of Soret & Dufour effect","authors":"Shilpa Choudhary , Ruchika Mehta , Tripti Mehta","doi":"10.1016/j.padiff.2025.101294","DOIUrl":"10.1016/j.padiff.2025.101294","url":null,"abstract":"<div><div>This research presents a comparative analysis of Cross diffusion effect on 2D MHD chemical reactive Williamson hybrid nanofluid (<em>MoS</em><sub>2</sub> − <em>GO</em>/<em>Methanol</em>) on a moving thin needle with thermal radiation. The main aim of this study is to increase the thermal efficiency using two different categories of nanoparticles: <em>MoS</em><sub>2</sub> − <em>GO</em>, with <em>Methanol</em> serving as the original liquid is calculated. PDEs can be changed into ordinary differential equations with the help of similarity substitution. Which are nonlinear, and the bvp4c technique is used to numerically simplify it. The results of this investigation indicate that the velocity profile of <em>GO</em>/<em>Methanol</em> composite nanofluid increases more than that of <em>MoS</em><sub>2</sub> − <em>GO</em>/<em>Methanol</em> through the increasing amount of Grashof number and Weissenberg parameter, even as the magnetic parameter and porosity impact have the opposite effect. On other hand, the chemical reaction and Schmidt number increase the rate of mass transfer for both nanofluids. The larger values of thermal radiation and Dufour effect enhance the thermal profile.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101294"},"PeriodicalIF":0.0,"publicationDate":"2025-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144917796","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}
The Benjamin-Bhona-Mahony equation is a non-linear partial differential equation arising in the study of waves, oceanography, Plasma physics, and shallow water theory. In the present work, we looked at the approximate solution of non-linear Benjamin-Bona-Mahony (BBM) problem by the Optimal Homotopy Asymptotic Method with Daftardar Jeffery Polynomials (OHAM-DJ). The BBM result is compared to analytic evaluation, the Homotopy Perturbation Technique (HPM), the Adomian Decomposition Method (ADM), and the Optimal Homotopy Asymptotic Method (OHAM-DJ). Figures of precise versus approximate solutions are also created, and it is established that OHAM-DJ's solution is substantially closer to the approximative than the precise. Additionally, the outcome demonstrates the effectiveness, simplicity, ease of use, and explicitness of OAM-DJ and provides a good means of controlling the convergence of approximations.
{"title":"Application of optimal homotopy asymptotic method with use of Daftardar Jeffery Polynomials to Benjamin-Bona-Mahony equation","authors":"Showkat Ahmad Lone , Rawan Bossly , M.M. Seada , Anwar Saeed","doi":"10.1016/j.padiff.2025.101282","DOIUrl":"10.1016/j.padiff.2025.101282","url":null,"abstract":"<div><div>The Benjamin-Bhona-Mahony equation is a non-linear partial differential equation arising in the study of waves, oceanography, Plasma physics, and shallow water theory. In the present work, we looked at the approximate solution of non-linear Benjamin-Bona-Mahony (BBM) problem by the Optimal Homotopy Asymptotic Method with Daftardar Jeffery Polynomials (OHAM-DJ). The BBM result is compared to analytic evaluation, the Homotopy Perturbation Technique (HPM), the Adomian Decomposition Method (ADM), and the Optimal Homotopy Asymptotic Method (OHAM-DJ). Figures of precise versus approximate solutions are also created, and it is established that OHAM-DJ's solution is substantially closer to the approximative than the precise. Additionally, the outcome demonstrates the effectiveness, simplicity, ease of use, and explicitness of OAM-DJ and provides a good means of controlling the convergence of approximations.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101282"},"PeriodicalIF":0.0,"publicationDate":"2025-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144917795","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}
Pub Date : 2025-08-22DOI: 10.1016/j.padiff.2025.101291
Pramod S , Sujatha N , Sreekala C. K , Hanumagowda B. N , Kiran S , Jagadish V. Tawade , Manish Gupta , Barno Abdullaeva , M. Ijaz Khan
This research paper comprehensively investigates magnetohydrodynamic free convection in a ferrofluid-filled rectangular cavity. The researchers designed a rectangular cavity where the left vertical wall maintains a warmer temperature than the right, while the horizontal walls (top and bottom) are adiabatic. A uniform magnetic field is imposed horizontally along the positive x-axis. The main objective is to analyse the impacts of various parameters, such as Hartmann number (0 ≤ Ha ≤ 60), Rayleigh number (103 ≤ Ra ≤ 106), and volume fraction (0 ≤ ϕ ≤ 0.04), on the heat transfer characteristics and fluid flow behavior within the enclosure. The governing equations are rigorously solved using the Galerkin finite element method. Quality plots like streamlines and isotherms and quantity plots like average Nusselt number (Nua) are presented to elucidate the underlying physics. The findings indicate that increasing Rayleigh numbers increases the convective flow, whereas increasing Hartmann numbers decreases the convective flow, promoting conduction as the primary mode of heat transfer. It is also notable that the inclusion of a magnetic field significantly alters the flow and temperature distributions, leading to a notable reduction in average Nusselt number. Furthermore, the incorporation of nanoparticles is found to intensify the heat transfer rates, with higher volume fractions yielding greater thermal performance. These findings offer significant implications for advancing thermal management, material processing techniques, and magnetohydrodynamic power generation, thereby providing innovative heat transfer solutions across diverse engineering applications.
{"title":"Magnetically driven free convection of nanofluids in rectangular cavities: A FEM approach","authors":"Pramod S , Sujatha N , Sreekala C. K , Hanumagowda B. N , Kiran S , Jagadish V. Tawade , Manish Gupta , Barno Abdullaeva , M. Ijaz Khan","doi":"10.1016/j.padiff.2025.101291","DOIUrl":"10.1016/j.padiff.2025.101291","url":null,"abstract":"<div><div>This research paper comprehensively investigates magnetohydrodynamic free convection in a ferrofluid-filled rectangular cavity. The researchers designed a rectangular cavity where the left vertical wall maintains a warmer temperature than the right, while the horizontal walls (top and bottom) are adiabatic. A uniform magnetic field is imposed horizontally along the positive <em>x-</em>axis. The main objective is to analyse the impacts of various parameters, such as Hartmann number (0 ≤ <em>Ha</em> ≤ 60), Rayleigh number (10<sup>3</sup> ≤ <em>Ra</em> ≤ 10<sup>6</sup>), and volume fraction (0 ≤ ϕ ≤ 0.04), on the heat transfer characteristics and fluid flow behavior within the enclosure. The governing equations are rigorously solved using the Galerkin finite element method. Quality plots like streamlines and isotherms and quantity plots like average Nusselt number (<em>Nu<sub>a</sub></em>) are presented to elucidate the underlying physics. The findings indicate that increasing Rayleigh numbers increases the convective flow, whereas increasing Hartmann numbers decreases the convective flow, promoting conduction as the primary mode of heat transfer. It is also notable that the inclusion of a magnetic field significantly alters the flow and temperature distributions, leading to a notable reduction in average Nusselt number. Furthermore, the incorporation of nanoparticles is found to intensify the heat transfer rates, with higher volume fractions yielding greater thermal performance. These findings offer significant implications for advancing thermal management, material processing techniques, and magnetohydrodynamic power generation, thereby providing innovative heat transfer solutions across diverse engineering applications.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101291"},"PeriodicalIF":0.0,"publicationDate":"2025-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144902467","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}
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