Partial Differential Equations in Applied Mathematics最新文献

{"title":"Investigating higher dimensional Jimbo–Miwa nonlinear dynamics through phase portraits, sensitivity, chaos and soliton behavior","authors":"Muhammad Aziz ur Rehman ,&nbsp;Muhammad Bilal Riaz ,&nbsp;Muhammad Iqbal","doi":"10.1016/j.padiff.2025.101101","DOIUrl":"10.1016/j.padiff.2025.101101","url":null,"abstract":"<div><div>The main focus of this article is on the development of new wave structures for the nonlinear (3+1)-dimensional Jimbo–Miwa equation. To solve the Jimbo–Miwa equation, a modified Khater method has been employed to generate various forms of soliton wave structures. Exact solutions to this equation are considered important for the complete understanding of the dynamics of waves in a physical model. The dynamic behavior of wave structures, including solutions for brilliant, single, dark, and periodic singular solitons, is enlightened by the obtained results. Selected solutions are plotted in both two- and three-dimensional graphs to illustrate their behavior. Furthermore, the system is converted into a planar dynamical system, and the derived solutions are examined using phase portraits to illustrate and demonstrate the theoretical results. Bifurcation and chaos theories are applied to enhance comprehension of the planar dynamical system that emerges from the examined system. Additionally, an investigation into the sensitivity of the provided model is conducted, revealing a moderate level of sensitivity and stability. These innovative concepts are utilized through symbolic computations to provide comprehensive and powerful mathematical tools for addressing various benign nonlinear problems.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101101"},"PeriodicalIF":0.0,"publicationDate":"2025-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143194093","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":"Analyzing radiative heat on third-grade fluids over an expanding inclined sheet subject to higher-order chemical reaction: An overlapping grid spectral quasilinearization approach","authors":"Titilayo M Agbaje ,&nbsp;Folarin Oluwaseun ,&nbsp;S.R. Mishra ,&nbsp;Rupa Baithalu ,&nbsp;Subhajit Panda","doi":"10.1016/j.padiff.2025.101098","DOIUrl":"10.1016/j.padiff.2025.101098","url":null,"abstract":"<div><div>Higher-order chemical reactions significantly enhance the concentration of the fluid indicating its vital role in processes involving radiative species. Therefore, the observation shows its important practical applications in industrial processes such as polymer extrusion, in which heat transfer properties are useful in the production of quality products. The proposed study emphases on the free convection of a third-grade fluid via an inclined expanding sheet for the influence of radiative heat and higher-order chemical reactions. However, the analysis incorporates the influence of viscous dissipation that is significant in determining the thermal behavior of the fluid. Further, the proposed flow phenomena governed by the set of partial differential equations are transformed into ordinary ones by the operating of suitable similarity rules. The transformed equations equipped with characterizing parameters are handled by a numerical technique known as the over lapping grid spectral quasilinearization method. The quantitative behavior of the factors intricate in it is deployed graphically and described briefly. However, the important outcomes of the study are; Richardson number is useful in enhancing the fluid momentum whereas the impact is reversed for the temperature and concentration distribution. Further, increasing heavier species i.e., Schmidt number attenuates the concentration profile.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101098"},"PeriodicalIF":0.0,"publicationDate":"2025-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143348056","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 symmetry reductions, solutions and conservation laws for a one-dimensional third-order Korteweg–de Vries equation with power law nonlinearity","authors":"Karabo Plaatjie ,&nbsp;Oscar Sivenathi Mbusi ,&nbsp;Chaudry Masood Khalique","doi":"10.1016/j.padiff.2025.101099","DOIUrl":"10.1016/j.padiff.2025.101099","url":null,"abstract":"<div><div>This work investigates a general form of one-dimensional Korteweg–de Vries (KdV) equation which arises in mathematical sciences. The model is examined for the first time with the use of techniques such as the symmetry method, direct integration procedure and explicit power series method. These methods provided us with new closed-form solutions of the one-dimensional third-order Korteweg–de Vries equation <span><span>(1.3)</span></span> in different forms. Each method employed here has its own merits. In addition, we include 2D and 3D graphical representations of selected exact solutions for specific parameter values to improve the reader’s understanding of these findings. Besides, for the first time conservation laws are presented in this work. We employ two different approaches, namely Noether’s theorem and multiplier method. The conserved vectors obtain contains conservation of momentum and energy.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101099"},"PeriodicalIF":0.0,"publicationDate":"2025-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143165076","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":"Rational hybrid block method for solving Bratu-type boundary value problems","authors":"S.S. Motsa ,&nbsp;S.D. Oloniiju ,&nbsp;H. Sithole-Mthethwa","doi":"10.1016/j.padiff.2025.101091","DOIUrl":"10.1016/j.padiff.2025.101091","url":null,"abstract":"<div><div>This study introduces a novel rational hybrid block method for solving Bratu-type boundary value problems, offering significant improvements in efficiency and accuracy. The method enhances the traditional block hybrid approach by incorporating rational approximations of grid points, which effectively reduce local truncation errors and improve numerical stability. Unlike existing methods, the proposed technique provides higher precision with fewer computational resources, making it particularly advantageous for problems requiring fine resolution. Extensive numerical experimentation on selected Bratu-type problems demonstrates superior performance in terms of convergence and accuracy, especially when using carefully optimized parameters. Moreover, the method’s robustness and adaptability make it well-suited for handling challenging problems, such as those involving bifurcations or steep gradients. These advantages position the method as a powerful tool for solving complex boundary value problems with broad applications in engineering and the physical sciences.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101091"},"PeriodicalIF":0.0,"publicationDate":"2025-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163947","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 effect on peristaltic motion of Williamson fluid via porous channel with suction and injection","authors":"K. Chakradhar ,&nbsp;K. Nandagopal ,&nbsp;Vishnudasu Prashanthi ,&nbsp;A. Parandhama ,&nbsp;T. Somaiah ,&nbsp;B.V. Sai Thrinath ,&nbsp;Nainaru Tarakaramu ,&nbsp;Ghulam Rasool ,&nbsp;Dilsora Abduvalieva","doi":"10.1016/j.padiff.2025.101103","DOIUrl":"10.1016/j.padiff.2025.101103","url":null,"abstract":"<div><div>Recent advancements in nanofluids (NFs) nanomaterials have led to diverse applications across multiple disciplines, enhancing heat transfer (HT) performance in clinical systems, engineering, cooling technologies, engine generators (EG), and more. These materials play a critical role in diagnosing underlying issues within human organs that rely on peristaltic pumping for fluid transfer, such as the stomach, intestines, and ureters. They are also integral to devices like flow meters, magnetohydrodynamic (MHD) generators and pumps, nuclear reactors using liquid metals, geothermal energy systems, and solar power absorbers. This research focuses on the influence of a magnetic field (MF) on peristaltic flow within a porous channel containing Williamson fluid (WF), driven by both injection and vertical pressure gradients. The objective is to analyze how peristaltic motion affects heat transfer efficiency in such systems. The fluid dynamics are modeled under the assumptions of long wavelengths and small Reynolds numbers. The study aims to evaluate key factors affecting pressure and frictional forces in the porous channel, including Hartmann number (HN), suction and injection parameters, and the rheological properties of Williamson fluid. Nonlinear differential equations governing the flow are solved analytically using perturbation techniques. The findings indicate that increasing the suction and injection parameters enhances volumetric flow rates, while the relationship between pressure rise and time-averaged volumetric flow rate is also explored. Results show that pressure rise decreases as the Hartmann number increases, consistent with the findings of Shapiro et al. The study concludes that the interaction between magnetic fields and peristaltic motion significantly influences fluid behavior, with potential applications in both biological and industrial systems.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101103"},"PeriodicalIF":0.0,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143164861","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":"Nonlinear dynamic evolution of a novel normalized time-fractional Burgers equation","authors":"Junseok Kim","doi":"10.1016/j.padiff.2025.101096","DOIUrl":"10.1016/j.padiff.2025.101096","url":null,"abstract":"<div><div>In this paper, a novel normalized time-fractional Burgers equation is proposed to enable a fair computational comparison study of its nonlinear dynamic evolution for various fractional order values. The introduced equation is formulated using a recently developed normalized time-fractional derivative, defined by the unique property that the sum of its weighting coefficients is equal to one. This ensures a well-balanced contribution of fractional terms, resulting in a normalized formulation that allows fair comparison. The classical Burgers equation is a basic partial differential equation (PDE) applied to model many physical phenomena such as traffic flow, gas dynamics and fluid dynamics, while the time-fractional Burgers equation is a modified form incorporating a fractional derivative in time to model diffusion and non-linear wave phenomena with memory effects. These memory effects are essential in accurately representing processes where the current state depends on the entire history of the system. We present several characteristic computational tests to study the effects of the time-fractional order. It is noteworthy that when a small time-fractional order is applied to an oscillatory advection velocity, increasing local maximum values may be observed as time progresses. This observation highlights the impact of the time-fractional order on the progression of the system’s dynamic features and provides valuable insights into how fractional derivatives influence the propagation and interaction of nonlinear waves in systems with memory.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101096"},"PeriodicalIF":0.0,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163945","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 Study of the anthrax transmission model in herbivorous animals involving vaccination and harvesting","authors":"Anita Triska ,&nbsp;Mona Zevika","doi":"10.1016/j.padiff.2025.101095","DOIUrl":"10.1016/j.padiff.2025.101095","url":null,"abstract":"<div><div>Caused by the bacterium <em>Bacillus anthracis</em>, anthrax is a serious zoonotic disease with a mortality rate of up to 60%. This disease naturally occurs in soil and commonly affects both domestic and wild animals worldwide. Humans are often infected with anthrax by consuming contaminated animal products. This research focuses on the transmission of anthrax to herbivorous animals, particularly livestock, by examining animal harvesting practices and efforts to prevent its spread through vaccination. The SVICA deterministic model was developed to better understand the transmission of anthrax by categorizing the population into susceptible, vaccinated, and infected animals, as well as carcasses and anthrax spores. The basic reproduction number (<span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>) is calculated using the NGM method to determine the outbreak threshold in a population. Additionally, the model analyzes the local stability of two disease-free equilibrium points when <span><math><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>&lt;</mo><mn>1</mn></mrow></math></span> and shows the existence of an endemic equilibrium point when <span><math><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>&gt;</mo><mn>1</mn></mrow></math></span>. Numerical exploration was conducted to examine the outbreak dynamics both generally and in specific cases. By varying the infection rate as a bifurcation parameter, it was found that when <span><math><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>&gt;</mo><mn>1</mn></mrow></math></span>, there is a stable interval and an unstable interval for the endemic equilibrium point, separated by the Hopf bifurcation curve. When the endemic equilibrium is unstable, a limit cycle occurs. Two distinct limit cycle behaviors were observed with different limit cycle trends. One case exhibited a more even rate of change, while the other displayed a slow–fast limit cycle, indicating a situation where anthrax cases remain low for a time but then increase drastically.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101095"},"PeriodicalIF":0.0,"publicationDate":"2025-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143194089","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":"Solving the Black–Scholes European options model using the reduced differential transform method with powered modified log-payoff function","authors":"S.E. Fadugba ,&nbsp;A.M. Udoye ,&nbsp;S.C. Zelibe ,&nbsp;S.O. Edeki ,&nbsp;C. Achudume ,&nbsp;A.A. Adeyanju ,&nbsp;O. Makinde ,&nbsp;P.A. Bankole ,&nbsp;M.C. Kekana","doi":"10.1016/j.padiff.2025.101087","DOIUrl":"10.1016/j.padiff.2025.101087","url":null,"abstract":"<div><div>This study introduces a novel analytical method for the Black–Scholes European options model, employing modified log-payoff functions raised to a power. The main motivation for this study stems from the need to develop more efficient and accurate analytical techniques for option pricing, particularly under the assumptions of the Black–Scholes framework. The proposed method utilizes the reduced differential transform method (RDTM), which provides a straightforward, flexible, and precise approach for solving the model. A significant contribution of this work is the ability to swiftly obtain explicit solutions with reduced computational time compared to traditional methods. The research also demonstrates that the sensitivities of the European call and put option prices, commonly known as the “Greeks,” can be effectively captured using this approach. Importantly, this model operates under the assumption that assets follow geometric Brownian motion and do not yield dividends. The findings from this study highlight the potential of RDTM as a powerful tool in the realm of financial mathematics, offering substantial improvements in the computational efficiency and accuracy of option pricing models.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101087"},"PeriodicalIF":0.0,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143165014","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 refactorization problems and rational Lax matrices of quadrirational Yang–Baxter maps","authors":"Pavlos Kassotakis ,&nbsp;Theodoros E. Kouloukas ,&nbsp;Maciej Nieszporski","doi":"10.1016/j.padiff.2025.101094","DOIUrl":"10.1016/j.padiff.2025.101094","url":null,"abstract":"<div><div>We present rational Lax representations for one-component parametric quadrirational Yang–Baxter maps in both the abelian and non-abelian settings. We show that from the Lax matrices of a general class of non-abelian involutive Yang–Baxter maps (<span><math><mi>K</mi></math></span>-list), by considering the symmetries of the <span><math><mi>K</mi></math></span>-list maps, we obtain compatible refactorization problems with rational Lax matrices for other classes of non-abelian involutive Yang–Baxter maps (<span><math><mi>Λ</mi></math></span>, <span><math><mi>H</mi></math></span> and <span><math><mi>F</mi></math></span> lists). In the abelian setting, this procedure generates rational Lax representations for the abelian Yang–Baxter maps of the <span><math><mi>F</mi></math></span> and <span><math><mi>H</mi></math></span> lists. Additionally, we provide examples of non-involutive (abelian and non-abelian) multi-parametric Yang–Baxter maps, along with their Lax representations, which lie outside the preceding lists.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101094"},"PeriodicalIF":0.0,"publicationDate":"2025-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163950","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":"Inclined magnetic fields heat transfer and thermal radiation on fractionalized EMHD Burgers’ fluid flow via bifurcated artery for tumor treatments","authors":"Isah Abdullahi ,&nbsp;D.G. Yakubu ,&nbsp;M.Y. Adamu ,&nbsp;Musa Ali ,&nbsp;A.M. Kwami","doi":"10.1016/j.padiff.2025.101093","DOIUrl":"10.1016/j.padiff.2025.101093","url":null,"abstract":"<div><div>In this study, we analyze the electro-magnetohydrodynamic (EMHD) blood flow through a bifurcated artery to enhance tumor treatments. We use the Atangana-Baleanu fractional derivative to model the EMHD blood flow of Burgers' fluid to obtain (derive) the non-dimensionalized form of the equations. Employing suitable variables, we transformed these modeled equations into ordinary differential equations. Analytical solutions of the transformed equations were computed using a combined Laplace transform and the classical method of undetermined coefficients. The results were simulated and presented graphically. The graphical results show that an increase in the Burgers’ parameter leads to a significant reduction in blood flow velocity from the central region of the artery towards the arterial wall, indicating the influence of viscoelastic properties on flow dynamics. Variations in the Eckert number and Joule heating parameters significantly affect blood flow temperature in the bifurcated artery, providing insights into enhancing advective heat transfer for effective tumor treatments and controlled heat management strategies. The findings revealed that increasing fractional parameter values result in a more gradual increase in concentration from the center towards the arterial wall. By exploring the intricate interplay of magnetic fields, heat radiation, Burgers' parameter, and fluid dynamics, this study contributes to advancements in biomedical engineering and medicine.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101093"},"PeriodicalIF":0.0,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143165072","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}