Partial Differential Equations in Applied Mathematics最新文献

A comparative study of numerical simulations via UAT and UAH tension B-splines for coupled Navier–Stokes equation with statistical validation

Partial Differential Equations in Applied Mathematics Pub Date : 2025-02-20 DOI: 10.1016/j.padiff.2025.101127

Mamta Kapoor

引用次数: 0

Viscous dissipation and Joule heating effects on MHD flow of blood-based hybrid nanofluid

Partial Differential Equations in Applied Mathematics Pub Date : 2025-02-19 DOI: 10.1016/j.padiff.2025.101130

Issah Imoro , Christian John Etwire , Rabiu Musah

{"title":"Viscous dissipation and Joule heating effects on MHD flow of blood-based hybrid nanofluid","authors":"Issah Imoro , Christian John Etwire , Rabiu Musah","doi":"10.1016/j.padiff.2025.101130","DOIUrl":"10.1016/j.padiff.2025.101130","url":null,"abstract":"<div><div>This study investigates the combined effects of viscous dissipation and Joule heating on the MHD flow of a blood-based hybrid nanofluid infused with Au and Cu nanoparticles. Governing equations are derived and appropriately normalized, with the Caputo fractional derivative applied to transform transient terms into time-fractional forms. These transformed equations, which yield complex modified Bessel functions, are then solved analytically using the Laplace transform method. The study’s primary novelty lies in the application of the concentrated matrix exponential (CME) method to numerically approximate inverse Laplace transforms of the modified equations, which is accomplished using Python software. Results for velocity, temperature, and nanoparticle distribution profiles are analyzed graphically. Numerical results for skin friction, Nusselt, and Sherwood numbers are also presented in a table. The results reveal that velocity, temperature, and hybrid nanoparticle distribution are greatly affected by the fractional-order parameter. Our results also show an enhancement in skin friction as Peclet, Eckert, and Reynolds numbers increase, with the reverse process observed for increasing Hartmann numbers, while Nusselt and Sherwood numbers decrease with increasing Reynolds numbers. Nanoparticles are redistributed at the core of the blood vessel rather than at the walls with the fractional-order parameter and Reynolds number, but remain constant throughout the vessel with the Hartmann, Peclet, and Eckert numbers. The findings of this study are essential in the medical field for targeted drug delivery and in treating burns, tumors, and cardiovascular disorders.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101130"},"PeriodicalIF":0.0,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143455028","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Solving a class of distributed-order time fractional wave-diffusion differential equations using the generalized fractional-order Bernoulli wavelets

Partial Differential Equations in Applied Mathematics Pub Date : 2025-02-18 DOI: 10.1016/j.padiff.2025.101131

Ali AbuGneam, Somayeh Nemati, Afshin Babaei

{"title":"Solving a class of distributed-order time fractional wave-diffusion differential equations using the generalized fractional-order Bernoulli wavelets","authors":"Ali AbuGneam, Somayeh Nemati, Afshin Babaei","doi":"10.1016/j.padiff.2025.101131","DOIUrl":"10.1016/j.padiff.2025.101131","url":null,"abstract":"<div><div>In this research, we propose a new numerical method for solving a class of distributed-order fractional partial differential equations, specifically focusing on distributed-order time fractional wave-diffusion equations. The method begins by introducing a novel generalization of Bernoulli wavelets and deriving an exact result for the Riemann–Liouville integral of these new basis functions. Utilizing the Gauss–Legendre quadrature formula and a strategically chosen set of collocation points, along with approximations for the unknown function and its derivatives, we transform the problem into a system of algebraic equations. An error analysis is then conducted for the approximation of a bivariate function using fractional-order Bernoulli wavelets. Finally, three examples are solved to demonstrate the method’s applicability and accuracy, with the numerical results confirming its effectiveness. These findings demonstrate that the parameters of the basis functions can be adjusted to suit the given problem, thereby enhancing the accuracy of the method.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101131"},"PeriodicalIF":0.0,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143455029","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Dynamics behavior of solitons based on exact solutions for the mathematical model arising in telecommunications

Partial Differential Equations in Applied Mathematics Pub Date : 2025-02-15 DOI: 10.1016/j.padiff.2025.101125

Ajay Kumar, Rahul Shukla

引用次数: 0

On the application of efficient block hybrid technique in solving strongly nonlinear oscillators

Partial Differential Equations in Applied Mathematics Pub Date : 2025-02-15 DOI: 10.1016/j.padiff.2025.101124

M.P. Mkhatshwa

{"title":"On the application of efficient block hybrid technique in solving strongly nonlinear oscillators","authors":"M.P. Mkhatshwa","doi":"10.1016/j.padiff.2025.101124","DOIUrl":"10.1016/j.padiff.2025.101124","url":null,"abstract":"<div><div>In this paper, an innovative block hybrid technique is proposed to solve strongly nonlinear oscillators. This numerical method utilizes a quasilinearization approach to linearize the nonlinear equations. The applicability and efficiency of this method is demonstrated by solving various test examples with oscillatory behavior. Theoretical analysis has been done by furnishing essential properties of the block hybrid method. The proposed method is bench-marked against the local linearization-based multi-domain spectral collocation method and ode45 MATLAB numerical solver. The results confirm that the numerical methods demonstrate good accuracy, numerical stability, and computational efficiency, with the proposed block hybrid method emerging as the most accurate, stable, and efficient iterative method that is zero-stable and converges very quickly. The enhanced accuracy is due to the incorporation of more intra-step points, resulting in higher-order truncation errors. However, superior numerical stability and computation efficiency are caused by the well-conditioned nature of the resulting coefficient matrix. In view of these advantages, the block hybrid method should be the preferred numerical method for solving strongly nonlinear equations, offering significant benefits in terms of accuracy, computational efficiency, numerical stability, and flexibility.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101124"},"PeriodicalIF":0.0,"publicationDate":"2025-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143429411","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Invariant analysis and equivalence transformations for the non-linear wave equation in elasticity

Partial Differential Equations in Applied Mathematics Pub Date : 2025-02-15 DOI: 10.1016/j.padiff.2025.101123

Akhtar Hussain

引用次数: 0

Numerical solution of two dimensional time-fractional telegraph equation using Chebyshev spectral collocation method

Partial Differential Equations in Applied Mathematics Pub Date : 2025-02-15 DOI: 10.1016/j.padiff.2025.101129

Kamran , Farman Ali Shah , Kamal Shah , Thabet Abdeljawad

{"title":"Numerical solution of two dimensional time-fractional telegraph equation using Chebyshev spectral collocation method","authors":"Kamran , Farman Ali Shah , Kamal Shah , Thabet Abdeljawad","doi":"10.1016/j.padiff.2025.101129","DOIUrl":"10.1016/j.padiff.2025.101129","url":null,"abstract":"<div><div>The 2D telegraph equation has numerous applications, such as signal processing, diffusion of biological species, and modeling wave propagation in electrical transmission lines. In this article, we present an efficient numerical scheme for solving the 2D time-fractional telegraph equation using a hybrid approach coupling the Laplace transform (LT) with the spectral collocation method based on Chebyshev nodes (ChSCM). The inclusion of the Caputo derivative in the classical telegraph equation provides a more accurate model for representing anomalous diffusion and wave propagation in heterogeneous media. The LT is employed to handle the time variable, transforming the considered equation into a system of spatial equations. These are then efficiently solved using the ChSCM. In the final step of our suggested approach, the numerical inversion of LT is performed to recover the solution in the time domain. This hybrid approach results in an efficient and robust numerical method. The convergence, accuracy, and stability of the method are verified using numerical examples. The acquired results show the potential of this numerical scheme for approximating the 2D time-fractional partial differential equations.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101129"},"PeriodicalIF":0.0,"publicationDate":"2025-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143429412","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Stability analysis and numerical simulations of a discrete-time epidemic model

Partial Differential Equations in Applied Mathematics Pub Date : 2025-02-14 DOI: 10.1016/j.padiff.2025.101118

Iqbal M. Batiha , Mohammad S. Hijazi , Amel Hioual , Adel Ouannas , Mohammad Odeh , Shaher Momani

{"title":"Stability analysis and numerical simulations of a discrete-time epidemic model","authors":"Iqbal M. Batiha , Mohammad S. Hijazi , Amel Hioual , Adel Ouannas , Mohammad Odeh , Shaher Momani","doi":"10.1016/j.padiff.2025.101118","DOIUrl":"10.1016/j.padiff.2025.101118","url":null,"abstract":"<div><div>This research investigates a discrete epidemic reaction–diffusion model, focusing on the nuances of both local and global stability. By employing second-order difference schemes alongside L1 approximations, we establish a robust numerical framework for simulating disease spread. The analysis begins with a thorough examination of two crucial equilibrium points: the disease-free equilibrium, which signifies complete eradication of the disease, and the endemic equilibrium, where the disease persists within the population. Through this exploration, we seek to identify the specific conditions that can lead to either successful containment or ongoing infection. To assess the global stability of the system, we utilize the Lyapunov method, a powerful analytical technique that enables us to derive sufficient conditions for global asymptotic stability. This rigorous methodology guarantees that, under defined conditions, the system will ultimately reach a stable equilibrium, irrespective of any initial perturbations. Complementing our theoretical framework, we conduct numerical simulations that validate our stability results. These simulations provide deeper insights into the system’s dynamic behavior, illustrating how various parameters and conditions influence its evolution. Moreover, the numerical simulations not only reinforce our theoretical findings but also facilitate the visualization and interpretation of the system’s complex dynamics. This synergy between analytical rigor and numerical validation enhances the reliability of our model, establishing it as a critical tool for understanding epidemic propagation and developing effective control strategies. Our comprehensive investigation thus enriches both the theoretical landscape of reaction–diffusion systems and their practical implications for managing disease outbreaks.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101118"},"PeriodicalIF":0.0,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143419214","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Modeling for the menstrual cycle with non-local operators

Partial Differential Equations in Applied Mathematics Pub Date : 2025-02-13 DOI: 10.1016/j.padiff.2025.101128

Jyoti Mishra

引用次数: 0

Computational approaches for singularly perturbed turning point problems with non-local boundary conditions

Partial Differential Equations in Applied Mathematics Pub Date : 2025-02-13 DOI: 10.1016/j.padiff.2025.101122

V. Raja , E. Sekar , K. Loganathan

引用次数: 0