Mathematical Methods in the Applied Sciences最新文献

{"title":"Propagation dynamics of a nonlocal dispersal Zika transmission model with general incidence","authors":"Juan He, Guo‐Bao Zhang","doi":"10.1002/mma.10466","DOIUrl":"https://doi.org/10.1002/mma.10466","url":null,"abstract":"In this paper, we are interested in propagation dynamics of a nonlocal dispersal Zika transmission model with general incidence. When the threshold is greater than one, we prove that there is a wave speed such that the model has a traveling wave solution with speed , and there is no traveling wave solution with speed less than . When the threshold is less than or equal to one, we show that there is no nontrivial traveling wave solution. The approaches we use here are Schauder's fixed point theorem with an explicit construction of a pair of upper and lower solutions, the contradictory approach, and the two‐sided Laplace transform.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220241","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On explicit ninth‐order, two‐step methods addressing y″=f(x,y)","authors":"Houssem Jerbi, Sondess Ben Aoun, Obaid Alshammari, Theodore E. Simos, Ch. Tsitouras, Mourad Kchaou","doi":"10.1002/mma.10448","DOIUrl":"https://doi.org/10.1002/mma.10448","url":null,"abstract":"We present a new family of ninth‐order hybrid explicit Numerov‐type methods, effectively utilizing only eight stages, for solving the special second‐order initial value problem. After applying a number of simplifying assumptions, we arrive to a reduced set of order conditions. Then, we derive an optimal method with constant coefficients that requires one less stage than standard methods found in the literature that use nine stages at this moment. Numerical tests are conducted using quadruple precision arithmetic on several well‐known problems and the superiority of the new method is clear. Finally, in Section 6, a Mathematica package is presented that implements the corresponding algorithm.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220242","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Product integration techniques for fractional integro‐differential equations","authors":"Sunil Kumar, Poonam Yadav, Vineet Kumar Singh","doi":"10.1002/mma.10464","DOIUrl":"https://doi.org/10.1002/mma.10464","url":null,"abstract":"This article presents an application of approximate product integration (API) to find the numerical solution of fractional order Volterra integro‐differential equation based on Caputo non‐integer derivative of order , where . Also, the idea is extended to a class of fractional order Volterra integro‐differential equation with a weakly singular kernel. For this purpose, two numerical schemes are established by utilizing the concept of the API method, and L1 and L1‐2 formulae. We applied L1 and L1‐2 discretization to approximate the Caputo non‐integer derivative. At the same time, Taylor's series expansion of an unknown function is taken into consideration when approximating the Volterra part in the considered mathematical model using the API method. Combination of API method with L1 and L1‐2 formula provided the order of convergence and for Scheme‐I and Scheme‐II, respectively. The derived techniques reduced the proposed model to a set of algebraic equations that can be resolved using well‐known numerical algorithms. Furthermore, the unconditional stability, convergence, and numerical stability of the formulated schemes have been rigorously investigated. Finally, we conducted some numerical experiments to validate our theoretical findings and guarantee the accuracy and efficiency of the recommended schemes. The comparison between the numerical outcomes obtained by proposed schemes and existing numerical techniques has also been provided through tables and graphs.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220239","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Data‐driven dynamical analysis of an age‐structured model: A graph‐theoretic approach","authors":"Preeti Deolia, Anuraj Singh","doi":"10.1002/mma.10445","DOIUrl":"https://doi.org/10.1002/mma.10445","url":null,"abstract":"The dynamics of the propagation and outspread of infectious diseases are eminently intricate, mainly due to the heterogeneity of the host individuals. In this paper, an age‐stratified SEIR (susceptible‐exposed‐infected‐recovered) epidemiological model incorporating saturated treatment function and heterogeneous contact rates is developed to study infectious disease transmission dynamics among various age groups. The expression for the basic reproduction number and conditions for the global stability of the system have been derived by a recently developed graph‐theoretic (GT) approach. Digraph reduction creates a GT version of the Gauss elimination method for computing the . The global dynamics results have been formed by constructing the Lyapunov function using a GT approach. The endemic equilibrium exists uniquely if , whereas the disease‐free equilibrium is observed to be globally stable if . The numerical simulations are demonstrated by extracting the daily reported COVID‐19 cases for the second wave in Italy. The age‐dependent contact matrix for the Republic of Italy (data sourced from the POLYMOD study) is computed via paper–diary methodology (PDM) grounded on a population‐prospective survey in European countries. Our numerical findings imply that (i) for the age group (20–49) years and (50–69) years, the number of infected persons is quite double as compared with the exposed cases; (ii) approximately 50% of positive cases lies in (20–69) years age group; (iii) for the (00–19) years age group, only half of the exposed individuals got infected; and (iv) a consistent graph is detected for the age group of (70–99) years in both cases; it shows that almost all the exposed got infected.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220090","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Solvability of a Hadamard fractional boundary value problem with multi-term integral and Hadamard fractional derivative boundary conditions","authors":"Tugba Senlik Cerdik","doi":"10.1002/mma.10475","DOIUrl":"10.1002/mma.10475","url":null,"abstract":"<p>In the present paper, we construct the existence of nontrivial solutions to a new kind of Hadamard fractional boundary value problem on an unbounded domain. With the contribution of some fixed point theorems in cone and the corresponding Green function, we ensure sufficient conditions for the Hadamard fractional boundary value problem. Also, the paper concludes with two examples to demonstrate our results.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220240","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Parallel inertial forward–backward splitting methods for solving variational inequality problems with variational inclusion constraints","authors":"Tran Van Thang, Ha Manh Tien","doi":"10.1002/mma.10356","DOIUrl":"https://doi.org/10.1002/mma.10356","url":null,"abstract":"The inertial forward–backward splitting algorithm can be considered as a modified form of the forward–backward algorithm for variational inequality problems with monotone and Lipschitz continuous cost mappings. By using parallel and inertial techniques and the forward–backward splitting algorithm, in this paper, we propose a new parallel inertial forward–backward splitting algorithm for solving variational inequality problems, where the constraints are the intersection of common solution sets of a finite family of variational inclusion problems. Then, strong convergence of proposed iteration sequences is showed under standard assumptions imposed on cost mappings in a real Hilbert space. Finally, some numerical experiments demonstrate the reliability and benefits of the proposed algorithm.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220243","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Variations of heat equation on the half-line via the Fokas method","authors":"Andreas Chatziafratis,&nbsp;Athanasios S. Fokas,&nbsp;Elias C. Aifantis","doi":"10.1002/mma.10303","DOIUrl":"10.1002/mma.10303","url":null,"abstract":"<p>In this review paper, we discuss some of our recent results concerning the rigorous analysis of initial boundary value problems (IBVPs) and newly discovered effects for certain evolution partial differential equations (PDEs). These equations arise in the applied sciences as models of phenomena and processes pertaining, for example, to continuum mechanics, heat-mass transfer, solid–fluid dynamics, electron physics and radiation, chemical and petroleum engineering, and nanotechnology. The mathematical problems we address include certain well-known classical variations of the traditional heat (diffusion) equation, including (i) the Sobolev–Barenblatt pseudoparabolic PDE (or modified heat or second-order fluid equation), (ii) a fourth-order heat equation and the associated Cahn–Hilliard (or Kuramoto–Sivashinsky) model, and (iii) the Rubinshtein–Aifantis double-diffusion system. Our work is based on the synergy of (i) the celebrated Fokas unified transform method (UTM) and (ii) a new approach to the rigorous analysis of this method recently introduced by one of the authors. In recent works, we considered forced versions of the aforementioned PDEs posed in a spatiotemporal quarter-plane with arbitrary, fully non-homogeneous initial and boundary data, and we derived formally effective solution representations, for the first time in the history of the models, justifying a posteriori their validity. This included the reconstruction of the prescribed initial and boundary conditions, which required careful analysis of the various integral terms appearing in the formulae, proving that they converge in a strictly defined sense. In each IBVP, the novel formula was utilized to rigorously deduce the solution's regularity properties near the boundaries of the spatiotemporal domain. Importantly, this analysis is indispensable for proving (non)uniqueness of solution. These works extend previous investigations. The usefulness of our closed-form solutions will be demonstrated by studying their long-time asymptotics. Specifically, we will briefly review some asymptotic results about Barenblatt's equation.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220244","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Extinction and stationary distribution of stochastic hepatitis B virus model","authors":"C. Gokila, M. Sambath","doi":"10.1002/mma.10467","DOIUrl":"https://doi.org/10.1002/mma.10467","url":null,"abstract":"In this article, we develop a Hepatitis B virus model with six compartments affected by environmental fluctuations since the Hepatitis B virus produces serious liver infections in the human body, putting many people at high risk. The existence of a global positive solution is shown to prove the positivity of solutions. We demonstrate that the system experiences the extinction property for a specific parametric restriction. Besides that, we obtain the stochastic stability region for the proposed model through the stationary distribution. To determine the appearance and disappearance of infection in the population, we find and analyze the reproduction ratio . In addition, we have verified the condition of the reproduction ratio through the graphical simulations.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220245","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The multigrid discretization of mixed discontinuous Galerkin method for the biharmonic eigenvalue problem","authors":"Jinhua Feng, Shixi Wang, Hai Bi, Yidu Yang","doi":"10.1002/mma.10455","DOIUrl":"https://doi.org/10.1002/mma.10455","url":null,"abstract":"The Ciarlet–Raviart mixed method is popular for the biharmonic equations/eigenvalue problem. In this paper, we propose a multigrid discretization based on the shifted‐inverse iteration of Ciarlet–Raviart mixed discontinuous Galerkin method for the biharmonic eigenvalue problem. We prove the a priori error estimates of the approximate eigenpairs. We also give the a posteriori error estimates of the approximate eigenvalues and prove the reliability of the estimator and implement adaptive computation. Numerical experiments show that our method can efficiently compute biharmonic eigenvalues.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220246","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dynamical bifurcations in a delayed fractional‐order neural network involving neutral terms","authors":"Chengdai Huang, Lei Fu, Shuang Liu, Jinde Cao, Mahmoud Abdel‐Aty, Heng Liu","doi":"10.1002/mma.10434","DOIUrl":"https://doi.org/10.1002/mma.10434","url":null,"abstract":"The stability and bifurcations of a fractional‐order neural network with a neutral delay are nicely contemplated with the help of the Cramer's rule. The three‐neuron neutral‐type fractional‐order neural network (NTFONN) is firstly constructed. Secondly, the Laplace transform of the Caputo fractional‐order derivatives is used. Afterward, using the analytical method of characteristic equations and Cramer's rule, the existence of Hopf bifurcations is obtained. Moreover, it indicates that the neutral delay plays an enormously significant role in remaining network stabilization and controlling the occurrence of Hopf bifurcations in NTFONN. It further detects that the devised NTFONN has outstanding stability performance in comparison with the corresponding integer‐order one. Finally, numerical simulations are developed to confirm the feasibility and validity of the obtained results.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220248","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}