Mathematical Methods in the Applied Sciences最新文献

英文中文

Propagation dynamics of a nonlocal dispersal Zika transmission model with general incidence 具有一般发病率的非本地分散寨卡传播模型的传播动力学

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences

Pub Date : 2024-09-10 DOI: 10.1002/mma.10466

Juan He, Guo‐Bao Zhang

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.

在本文中，我们关注的是具有一般发生率的非局部扩散寨卡病毒传播模型的传播动力学。当阈值大于 1 时，我们证明存在一个波速，使得模型有一个速度为、的行波解，并且不存在速度小于、的行波解。当阈值小于或等于 1 时，我们证明不存在非小的行波解。我们在此使用的方法有：明确构造一对上解和下解的 Schauder 定点定理、矛盾方法和双面拉普拉斯变换。

引用次数: 0

On explicit ninth‐order, two‐step methods addressing y″=f(x,y) 关于处理 y″=f(x,y) 的显式九阶两步法

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences

Pub Date : 2024-09-10 DOI: 10.1002/mma.10448

Houssem Jerbi, Sondess Ben Aoun, Obaid Alshammari, Theodore E. Simos, Ch. Tsitouras, Mourad Kchaou

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.

我们提出了一种新的九阶混合显式 Numerov 型方法系列，只需有效利用八个阶段，即可求解特殊的二阶初值问题。在应用了一系列简化假设后，我们得出了一组简化的阶次条件。然后，我们推导出一种具有常数系数的最优方法，它比目前文献中使用九级的标准方法少用一级。我们使用四倍精度算术对几个著名问题进行了数值测试，新方法的优越性显而易见。最后，在第 6 节中介绍了实现相应算法的 Mathematica 软件包。

引用次数: 0

Product integration techniques for fractional integro‐differential equations 分数积分微分方程的乘积积分技术

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences

Pub Date : 2024-09-10 DOI: 10.1002/mma.10464

Sunil Kumar, Poonam Yadav, Vineet Kumar Singh

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.

本文介绍了基于卡普托非整数导数的分数阶 Volterra 积分微分方程的近似积积分（API）数值解。此外，这一想法还扩展到一类具有弱奇异内核的分数阶 Volterra 积分微分方程。为此，我们利用 API 方法的概念以及 L1 和 L1-2 公式建立了两种数值方案。我们采用 L1 和 L1-2 离散法来逼近 Caputo 非整数导数。同时，在使用 API 方法近似所考虑的数学模型中的 Volterra 部分时，考虑了未知函数的泰勒级数展开。API 方法与 L1 和 L1-2 公式相结合，分别为方案一和方案二提供了收敛阶次。推导出的技术将所提出的模型简化为一组代数方程，可以使用著名的数值算法进行求解。此外，我们还对所制定方案的无条件稳定性、收敛性和数值稳定性进行了严格研究。最后，我们进行了一些数值实验，以验证我们的理论发现，并保证推荐方案的准确性和效率。我们还通过表格和图表对建议方案与现有数值技术的数值结果进行了比较。

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引用次数: 0

Data‐driven dynamical analysis of an age‐structured model: A graph‐theoretic approach 年龄结构模型的数据驱动动态分析：图论方法

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences

Pub Date : 2024-09-09 DOI: 10.1002/mma.10445

Preeti Deolia, Anuraj Singh

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.

主要由于宿主个体的异质性，传染病的传播和扩散动态错综复杂。本文建立了一个年龄分层的 SEIR（易感-暴露-感染-康复）流行病学模型，该模型包含饱和治疗函数和异质性接触率，用于研究传染病在不同年龄组之间的传播动态。基本繁殖数的表达式和系统全局稳定性的条件是通过最近开发的图论（GT）方法推导出来的。数图还原法是高斯消除法的 GT 版本，用于计算系统的全局稳定性。全局动力学结果是通过使用 GT 方法构建 Lyapunov 函数得出的。如果......，则地方病平衡唯一存在，而如果......，则无病平衡是全局稳定的。通过提取意大利第二波 COVID-19 的每日报告病例，对数值模拟进行了演示。意大利共和国与年龄相关的接触矩阵（数据来源于 POLYMOD 研究）是通过基于欧洲国家人口前瞻性调查的纸质日记法（PDM）计算得出的。我们的数字研究结果表明：(i) 在（20-49）岁和（50-69）岁年龄组中，感染者人数是暴露病例人数的两倍；(ii) 约 50%的阳性病例发生在（20-69）岁年龄组；(iii) 在（00-19）岁年龄组中，只有一半的暴露者受到感染；(iv) 在（70-99）岁年龄组中，两种情况下都发现了一致的图形；这表明几乎所有暴露者都受到感染。

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引用次数: 0

Solvability of a Hadamard fractional boundary value problem with multi-term integral and Hadamard fractional derivative boundary conditions 具有多期积分和哈达玛分数导数边界条件的哈达玛分数边界值问题的可解性

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences

Pub Date : 2024-09-09 DOI: 10.1002/mma.10475

Tugba Senlik Cerdik

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.

在本文中，我们构建了无界域上一种新型哈达玛德分数边界值问题的非小解的存在性。借助锥定点定理和相应的格林函数，我们确保了 Hadamard 分数边界值问题的充分条件。最后，本文还通过两个例子来证明我们的结果。

引用次数: 0

Parallel inertial forward–backward splitting methods for solving variational inequality problems with variational inclusion constraints 用于求解具有变式包容约束的变式不等式问题的并行惯性前向后向分裂方法

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences

Pub Date : 2024-09-09 DOI: 10.1002/mma.10356

Tran Van Thang, Ha Manh Tien

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.

惯性前向后拆分算法可以看作是前向后算法的一种改进形式，用于求解具有单调和Lipschitz连续代价映射的变分不等式问题。本文利用并行和惯性技术以及前向后分算法，提出了一种新的并行惯性前向后分算法，用于求解变分不等式问题，其中约束条件是有限变分包含问题族的公共解集的交集。然后，在对实希尔伯特空间中的代价映射施加标准假设的情况下，证明了所提出的迭代序列具有很强的收敛性。最后，一些数值实验证明了所提算法的可靠性和优势。

引用次数: 0

Variations of heat equation on the half-line via the Fokas method 通过福卡斯方法对半线上的热方程进行变分

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences

Pub Date : 2024-09-08 DOI: 10.1002/mma.10303

Andreas Chatziafratis, Athanasios S. Fokas, Elias C. Aifantis

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.

在这篇综述论文中，我们讨论了我们最近在严格分析初始边界值问题（IBVPs）和某些演化偏微分方程（PDEs）的新发现效应方面取得的一些成果。这些方程作为现象和过程的模型出现在应用科学领域，例如连续介质力学、热-质传递、固体-流体动力学、电子物理和辐射、化学和石油工程以及纳米技术。我们研究的数学问题包括传统热（扩散）方程的某些著名经典变体，包括 (i) Sobolev-Barenblatt 伪抛物 PDE（或修正热方程或二阶流体方程），(ii) 四阶热方程和相关的 Cahn-Hilliard（或 Kuramoto-Sivashinsky）模型，以及 (iii) Rubinshtein-Aifantis 双扩散系统。我们的工作基于 (i) 著名的福卡斯统一变换方法 (UTM) 和 (ii) 作者之一最近提出的对该方法进行严格分析的新方法的协同作用。在最近的研究中，我们考虑了在时空四分之一平面上以任意、完全非均质的初始数据和边界数据求解的上述 PDE 的强制版本，并在模型历史上首次正式导出了有效的解表示，证明了它们的后验有效性。这包括重构规定的初始条件和边界条件，这需要仔细分析公式中出现的各种积分项，证明它们在严格定义的意义上收敛。在每个 IBVP 中，新公式都被用来严格推导时空域边界附近解的正则特性。重要的是，这种分析对于证明解的（非）唯一性是不可或缺的。这些工作扩展了之前的研究。我们将通过研究闭式解的长期渐近性来证明其实用性。具体来说，我们将简要回顾有关巴伦布拉特方程的一些渐近结果。

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引用次数: 0

Extinction and stationary distribution of stochastic hepatitis B virus model 随机乙型肝炎病毒模型的消亡和静态分布

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences

Pub Date : 2024-09-06 DOI: 10.1002/mma.10467

C. Gokila, M. Sambath

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.

由于乙型肝炎病毒会在人体内产生严重的肝脏感染，使许多人处于高风险之中，因此我们在本文中建立了一个乙型肝炎病毒模型，其中包含六个受环境波动影响的分区。全局正解的存在证明了解的实在性。我们证明了该系统在特定参数限制下的消亡特性。此外，我们还通过静态分布获得了所提模型的随机稳定区域。为了确定感染在种群中的出现和消失，我们找到并分析了繁殖率。此外，我们还通过图形模拟验证了繁殖率的条件。

引用次数: 0

The multigrid discretization of mixed discontinuous Galerkin method for the biharmonic eigenvalue problem 双谐波特征值问题的混合非连续伽勒金方法的多网格离散化

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences

Pub Date : 2024-09-06 DOI: 10.1002/mma.10455

Jinhua Feng, Shixi Wang, Hai Bi, Yidu Yang

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.

Ciarlet-Raviart 混合法是双谐波方程/特征值问题的常用方法。本文针对双谐波特征值问题，提出了一种基于 Ciarlet-Raviart 混合非连续 Galerkin 方法移反迭代的多网格离散化方法。我们证明了近似特征对的先验误差估计。我们还给出了近似特征值的后验误差估计，证明了估计器的可靠性，并实现了自适应计算。数值实验表明，我们的方法可以高效地计算双谐波特征值。

引用次数: 0

Dynamical bifurcations in a delayed fractional‐order neural network involving neutral terms 涉及中性项的延迟分数阶神经网络的动态分岔

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences

Pub Date : 2024-09-05 DOI: 10.1002/mma.10434

Chengdai Huang, Lei Fu, Shuang Liu, Jinde Cao, Mahmoud Abdel‐Aty, Heng Liu

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.

在克拉默法则的帮助下，很好地探讨了具有中性延迟的分数阶神经网络的稳定性和分岔问题。首先构建了三神经元中性型分数阶神经网络（NTFONN）。其次，使用卡普托分数阶导数的拉普拉斯变换。然后，利用特征方程解析法和克拉默法则，得到霍普夫分岔的存在性。此外，研究还表明，中性延迟在 NTFONN 中保持网络稳定和控制霍普夫分岔的发生方面起着非常重要的作用。研究进一步发现，与相应的整数阶 NTFONN 相比，所设计的 NTFONN 具有出色的稳定性能。最后，通过数值模拟证实了所获结果的可行性和有效性。

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