Applied Numerical Mathematics最新文献

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Numerical simulation of a dynamic human capital model with demographic delays via the local discrete Galerkin method 基于局部离散伽辽金方法的人口统计学时滞动态人力资本模型数值模拟

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics

Pub Date : 2025-06-20 DOI: 10.1016/j.apnum.2025.06.007

Yadollah Ordokhani , Alireza Hosseinian , Pouria Assari

A strong and dynamic economy depends on various factors, with human capital playing a crucial role in fostering resilience and adaptability in an ever-changing world. Human capital, which depends on the past behavior of the system, requires strategic investments in education, health, and skill development. This study presents a numerical approach for solving the human capital model with age-structured delays, formulated as integro-differential equations with double delays and difference kernels. The proposed method employs a local meshless discrete Galerkin approach based on the moving least squares (MLS) technique, which can work with irregular or non-uniform data. The localized nature of the MLS scheme enhances computational efficiency by focusing on small neighborhoods. Moreover, the stabilized MLS framework, achieved by using shifted and scaled polynomial basis functions, enhances numerical stability and reduces sensitivity to the distribution of nodes, thereby transferring these advantageous properties to the method. The simplicity of the proposed algorithm makes it easy to implement on standard personal computers and extend to a wider class of delay integro-differential equations. To assess its reliability, we analyzed its error and determined the convergence order of the presented method. We have applied it to solve several numerical examples, and the obtained results confirm the method's accuracy, stability, and alignment with theoretical findings.

一个强大而充满活力的经济取决于各种因素，而人力资本在培养适应不断变化的世界的韧性和适应性方面发挥着至关重要的作用。人力资本取决于系统过去的行为，需要在教育、卫生和技能发展方面进行战略投资。本文提出了一种求解具有年龄结构延迟的人力资本模型的数值方法，该模型被表述为具有双延迟和差分核的积分-微分方程。该方法采用基于移动最小二乘（MLS）技术的局部无网格离散伽辽金方法，可以处理不规则或非均匀数据。MLS方案的局部特性通过关注小邻域来提高计算效率。此外，通过使用移位和缩放的多项式基函数实现的稳定MLS框架提高了数值稳定性，降低了对节点分布的敏感性，从而将这些优点转移到该方法中。该算法的简单性使其易于在标准个人计算机上实现，并扩展到更广泛的延迟积分微分方程。为了评估其可靠性，我们分析了该方法的误差，并确定了该方法的收敛顺序。应用该方法对若干数值算例进行了求解，得到的结果证实了该方法的准确性、稳定性以及与理论结果的一致性。

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引用次数: 0

Note on an inertial projection-based approach for solving extended general quasi-variational inequalities and its convergence analysis 基于惯性投影的广义拟变分不等式求解方法及其收敛性分析

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics

Pub Date : 2025-06-20 DOI: 10.1016/j.apnum.2025.06.012

Saudia Jabeen , Siegfried Macías , Saleem Ullah , Muhammad Aslam Noor , Jorge E. Macías-Díaz

In this work, an inertial projection-based method is proposed to find approximate solutions to a new class of quasi-variational inequalities. The approach utilizes projection techniques to develop an iterative scheme, and its convergence properties are rigorously examined under appropriate conditions. Various specific cases are derived from the general framework, highlighting the adaptability of the proposed method. The comparative performance of this approach with existing techniques remains an open area for exploration. It is expected that the theoretical framework and techniques proposed in this study will stimulate further research in this domain.

在这项工作中，提出了一种基于惯性投影的方法来求一类新的拟变分不等式的近似解。该方法利用投影技术开发迭代格式，并在适当的条件下严格检验了其收敛性。从总体框架中衍生出各种具体案例，突出了所提方法的适应性。这种方法与现有技术的性能比较仍然是一个有待探索的开放领域。期望本研究提出的理论框架和技术将促进该领域的进一步研究。

引用次数: 0

Analysis of Tseng algorithm with inertial extrapolation step for stochastic variational inequality problem 随机变分不等式问题的惯性外推Tseng算法分析

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics

Pub Date : 2025-06-20 DOI: 10.1016/j.apnum.2025.06.008

Olawale K. Oyewole , Seithuti P. Moshokoa , Sani Salisu , Yekini Shehu

In this paper, we design an inertial version of the Tseng extragradient algorithm (also called the Forward-Backward-Forward Algorithm) with self-adaptive step sizes to solve the stochastic variational inequality problem. We prove that the sequence of iterates generated by our proposed algorithm converges to a solution of the stochastic variational inequality problem under mild conditions. Furthermore, we obtain some convergence rates and numerical simulations of our proposed algorithm with comparisons with related algorithms to show the superiority of our algorithm.

本文设计了一种具有自适应步长的惯性版本的Tseng extraggradient算法（也称为Forward-Backward-Forward算法）来解决随机变分不等式问题。证明了该算法生成的迭代序列在温和条件下收敛于随机变分不等式问题的一个解。最后给出了算法的一些收敛速度和数值模拟，并与相关算法进行了比较，证明了算法的优越性。

引用次数: 0

An efficient multi projection methods for systems of Fredholm integral equations with mixed weakly singular kernels: A superconvergence approach 混合弱奇异核Fredholm积分方程组的一种有效多投影方法：一种超收敛方法

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics

Pub Date : 2025-06-19 DOI: 10.1016/j.apnum.2025.06.006

Krishna Murari Malav , Kapil Kant , Joydip Dhar , Samiran Chakraborty

In this article, we develop the multi-Galerkin and iterated multi-Galerkin methods to solve systems of second-kind linear Fredholm integral equations (FIEs) with smooth and mixed weakly singular kernels. First, we develop the mathematical formulation of the multi-Galerkin and iterated multi-Galerkin methods using piecewise polynomial approximations to solve such systems and obtain superconvergence results. These methods transform the linear system of FIEs into corresponding matrix equations. We derive error estimates and obtain the convergence analysis. We prove that the convergence rates for the multi-Galerkin method are

O (h^{3 r})

for smooth kernels and

O (h^{1 + r - α} \log h)

for mixed weakly singular kernels, where r denote the degree of the piecewise polynomials, h is the norm of partitions and

α = \max_{i, j} α_{i j}

. Moreover, we establish that the iterated multi-Galerkin method achieves improved convergence rates of

O (h^{4 r})

for smooth kernels and

O (h^{r + 2 (1 - α)} {(\log h)}^{2})

for mixed weakly singular kernels. Hence, the results show that the iterated multi-Galerkin method improves the multi-Galerkin method. Finally, the theoretical results are validated through the numerical examples.

利用多重galerkin和迭代多重galerkin方法，求解了一类具有光滑和混合弱奇异核的第二类线性Fredholm积分方程组。首先，我们利用分段多项式逼近建立了多重galerkin和迭代多重galerkin方法的数学表达式，并得到了超收敛结果。这些方法将FIEs的线性方程组转化为相应的矩阵方程。我们推导了误差估计，并得到了收敛性分析。证明了多重伽辽金方法对于光滑核的收敛速度为O(h3r)，对于混合弱奇异核的收敛速度为O(h1+r−αlog (h))，其中r表示分段多项式的阶数，h表示分区范数，α=maxi,j∈αij。此外，我们还证明了迭代多重伽辽金方法对于光滑核的收敛速度为O(h4r)，对于混合弱奇异核的收敛速度为O(hr+2（1−α)(log (h)2)）。结果表明，迭代多重伽辽金方法是对多重伽辽金方法的改进。最后通过数值算例对理论结果进行了验证。

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引用次数: 0

Localization of tumor through a non-conventional numerical shape optimization technique 利用非常规数值形状优化技术对肿瘤进行定位

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics

Pub Date : 2025-06-16 DOI: 10.1016/j.apnum.2025.06.005

Julius Fergy Tiongson Rabago

This paper presents a method for estimating the shape and location of an embedded tumor using shape optimization techniques, specifically through the coupled complex boundary method. The inverse problem—characterized by a measured temperature profile and corresponding heat flux (e.g., from infrared thermography)—is reformulated as a complex boundary value problem with a complex Robin boundary condition, thereby simplifying its over-specified nature. The geometry of the tumor is identified by optimizing an objective functional that depends on the imaginary part of the solution throughout the domain. The shape derivative of the functional is derived through shape sensitivity analysis. An iterative algorithm is developed to numerically recover the tumor shape, based on the Riesz representative of the gradient and implemented using the finite element method. In addition, the mesh sensitivity of the finite element solution to the state problem is analyzed, and bounds are established for its variation with respect to mesh deformation and its gradient. Numerical examples are presented to validate the theoretical results and to demonstrate the accuracy and effectiveness of the proposed method.

本文提出了一种利用形状优化技术，特别是通过耦合复杂边界方法来估计嵌入肿瘤的形状和位置的方法。反问题——以测量的温度剖面和相应的热通量（例如，来自红外热成像）为特征——被重新表述为具有复杂Robin边界条件的复杂边值问题，从而简化了其过度指定的性质。通过优化目标函数来识别肿瘤的几何形状，目标函数依赖于整个域内解的虚部。通过形状灵敏度分析，导出了泛函的形状导数。提出了一种基于Riesz梯度表示的肿瘤形状数值恢复迭代算法，并采用有限元法实现。此外，分析了状态问题有限元解的网格灵敏度，并建立了其随网格变形及其梯度变化的边界。数值算例验证了理论结果，验证了所提方法的准确性和有效性。

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引用次数: 0

A high-order accurate unconditionally stable bound-preserving numerical scheme for the Cahn-Hilliard-Navier-Stokes equations Cahn-Hilliard-Navier-Stokes方程的高阶精确无条件稳定保界数值格式

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics

Pub Date : 2025-06-10 DOI: 10.1016/j.apnum.2025.06.004

Yali Gao , Daozhi Han , Sayantan Sarkar

A high order numerical method is developed for solving the Cahn-Hilliard-Navier-Stokes equations with the Flory-Huggins potential. The scheme is based on the

Q_{k}

finite element with mass lumping on rectangular grids, the second-order convex splitting method and the pressure correction method. The unique solvability, unconditional stability, and bound-preserving properties are rigorously established. The key for bound-preservation is the discrete

L^{1}

estimate of the singular potential. Ample numerical experiments are performed to validate the desired properties of the proposed numerical scheme.

提出了一种求解具有Flory-Huggins势的Cahn-Hilliard-Navier-Stokes方程的高阶数值方法。该方案基于矩形网格质量集总的Qk有限元、二阶凸分裂法和压力修正法。严格地建立了唯一可解性、无条件稳定性和保界性。保持边界的关键是奇异势的离散L1估计。进行了大量的数值实验来验证所提出的数值格式的预期性能。

引用次数: 0

Analysis of a divergence-free element-free Galerkin method for the Navier-Stokes equations Navier-Stokes方程的无散度无单元Galerkin方法分析

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics

Pub Date : 2025-06-10 DOI: 10.1016/j.apnum.2025.06.002

Xiaolin Li , Haiyun Dong

In this paper, an efficient divergence-free element-free Galerkin (DFEFG) method is proposed for the numerical analysis of the incompressible Navier-Stokes equations. In this method, a divergence-free moving least squares (DFMLS) approximation is used to obtain the meshless approximation of the divergence-free velocity field. The properties, stability and error of the DFMLS approximation are analyzed firstly, and then the stability and error estimation of the DFEFG method are derived theoretically. Finally, numerical results demonstrate the efficiency of the proposed methods and verify the theoretical analysis.

本文提出了一种有效的无散度无单元伽辽金（DFEFG）方法，用于不可压缩Navier-Stokes方程的数值分析。该方法采用无散度移动最小二乘（DFMLS）近似，得到无散度速度场的无网格近似。首先分析了DFMLS近似的性质、稳定性和误差，然后从理论上推导了DFEFG方法的稳定性和误差估计。最后，数值结果验证了所提方法的有效性和理论分析的正确性。

引用次数: 0

Generalized Clenshaw-Curtis quadrature method for systems of linear ODEs with constant coefficients 常系数线性微分方程系统的广义Clenshaw-Curtis正交法

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics

Pub Date : 2025-06-09 DOI: 10.1016/j.apnum.2025.06.003

Fu-Rong Lin, Xi Yang, Gui-Rong Zhang

In this paper, we consider high precision numerical methods for the initial problem of systems of linear ordinary differential equations (ODEs) with constant coefficients. It is well-known that the analytic solution of such a system of linear ODEs involves a matrix exponential function and an integral whose integrand is the product of a matrix exponential and a vector-valued function. We mainly consider numerical quadrature methods for the integral term in the analytic solution and propose a generalized Clenshaw-Curtis (GCC) quadrature method. The proposed method is then applied to the initial-boundary value problem for a heat conduction equation and a Riesz space fractional diffusion equation, respectively. Numerical results are presented to demonstrate the effectiveness of the proposed method.

本文研究了常系数线性常微分方程系统初始问题的高精度数值解法。众所周知，这种线性微分方程系统的解析解涉及一个矩阵指数函数和一个积分，其被积是一个矩阵指数函数和一个向量值函数的乘积。本文主要研究了解析解中积分项的数值求积分方法，提出了一种广义的clclenshaw - curtis求积分方法。然后将该方法分别应用于热传导方程和Riesz空间分数扩散方程的初边值问题。数值结果验证了该方法的有效性。

引用次数: 0

On steepest coordinate descent method for computing extreme eigenpairs of symmetric matrices 对称矩阵极值特征对的最陡坐标下降法

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics

Pub Date : 2025-06-09 DOI: 10.1016/j.apnum.2025.06.001

Zhong-Zhi Bai

For solving real and symmetric eigenvalue problems of huge sizes, we propose a steepest coordinate descent method, establish its convergence theory under reasonable conditions, and show its computational effectiveness by numerical experiments.

针对大型实数和对称特征值问题，提出了一种最陡坐标下降法，在合理条件下建立了最陡坐标下降法的收敛理论，并通过数值实验证明了其计算有效性。

引用次数: 0

A new error analysis of an explicit skeletal discontinuous Galerkin scheme for time-dependent Maxwell equations 时变Maxwell方程的显式骨架不连续Galerkin格式的新误差分析

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics

Pub Date : 2025-06-04 DOI: 10.1016/j.apnum.2025.05.011

Achyuta Ranjan Dutta Mohapatra, Bhupen Deka

This article focuses on the convergence analysis of second-order time-dependent Maxwell equations in conducting and non-conducting media. Firstly, the spatial discretization is made using a skeletal discontinuous Galerkin method, and then some essential tools are established to deduce the stability and error estimates. Under suitable regularity assumptions on initial data, stability and optimal convergence of the error are proved for the semi-discrete problem in a discretely defined

H (curl)

-norm. Next, temporal discretization is applied to the semi-discrete system by using the explicit Leap-frog schemes and optimal error bounds

O (τ^{2} + h^{k})

k \geq 1

is the degree of polynomial approximation, are achieved in the discrete energy norm. Finally, computational experiments are performed to validate the theoretical conclusions. Error analysis of explicit fully discrete schemes in polygonal/polyhedral meshes for the second-order Maxwell equations in a conducting media is missing in the literature, and we intend to fill this gap in the current article.

本文研究了二阶随时间变化的麦克斯韦方程组在导电介质和非导电介质中的收敛性分析。首先，采用骨架不连续伽辽金方法进行空间离散化，然后建立一些必要的工具来推导稳定性和误差估计。在适当的初始数据正则性假设下，证明了离散定义H（旋度）范数半离散问题的稳定性和误差的最优收敛性。其次，利用显式Leap-frog格式将时间离散化应用于半离散系统，并在离散能量范数中实现了最优误差界O(τ2+hk)， k≥1为多项式近似度。最后，通过计算实验对理论结论进行了验证。文献中缺少对导电介质中二阶麦克斯韦方程组的多边形/多面体网格中显式完全离散格式的误差分析，我们打算在本文中填补这一空白。

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