Results in Applied Mathematics最新文献

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A numerical method based on the shifted Jacobi polynomials for a class of tempered fractional quadratic integro-differential equations 一类缓变分数阶二次积分微分方程的基于移位Jacobi多项式的数值解法

IF 1.4 Q2 MATHEMATICS, APPLIED

Results in Applied Mathematics

Pub Date : 2025-06-13 DOI: 10.1016/j.rinam.2025.100601

P. Senfiazad , M.H. Heydari , M. Bayram , D. Baleanu

This paper introduces a new class of tempered fractional quadratic integro-differential equations using the Caputo fractional derivative. The existence and uniqueness of solutions to these equations are analyzed. A numerical method based on the shifted Jacobi polynomials is developed to solve these equations. To execute the proposed method, two operational matrices corresponding to the ordinary and Riemann–Liouville tempered fractional integrals of these polynomials are extracted. In the developed method, the tempered fractional derivative term is initially represented as a linear combination of the aforementioned polynomials with some unknown coefficients. Then, by applying the Riemann–Liouville tempered fractional integral to the expressed polynomials and utilizing their fractional integral operational matrix, an approximation of the unknown solution is defined based on these polynomials and the introduced coefficients. Subsequently, by substituting these approximations into the problem under consideration, and applying the operational matrix of ordinary integral to the shifted Jacobi polynomials, along with utilizing their orthogonality, an approximate solution to the original problem is obtained by solving a nonlinear system of algebraic equations. The convergence of the proposed method is analyzed theoretically and demonstrated through numerical examples. Furthermore, the stability of the solutions is analyzed.

本文利用Caputo分数阶导数引入了一类新的缓变分数阶二次积分微分方程。分析了这些方程解的存在唯一性。提出了一种基于移位雅可比多项式的数值求解方法。为了实现所提出的方法，提取了对应于这些多项式的普通积分和黎曼-刘维尔回火分数积分的两个运算矩阵。在所开发的方法中，缓和分数阶导数项最初表示为上述多项式与一些未知系数的线性组合。然后，将Riemann-Liouville调质分数阶积分应用于所表达的多项式，并利用其分数阶积分运算矩阵，基于这些多项式和引入的系数定义未知解的近似。随后，将这些近似代入所考虑的问题，并将普通积分的运算矩阵应用于移位的雅可比多项式，并利用它们的正交性，通过求解非线性代数方程组得到原问题的近似解。从理论上分析了该方法的收敛性，并通过数值算例进行了验证。进一步分析了解的稳定性。

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引用次数: 0

Convergence analysis of option drift rate inverse problem based on degenerate parabolic equation 基于退化抛物方程的期权漂移率反问题收敛性分析

IF 1.4 Q2 MATHEMATICS, APPLIED

Results in Applied Mathematics

Pub Date : 2025-05-01 DOI: 10.1016/j.rinam.2025.100561

Miao-miao Song , Zui-cha Deng , Xiang Li , Qiu Cui

In this paper, we study the convergence of the inverse drift rate problem of option pricing based on degenerate parabolic equations, aiming to recover the stock price drift rate function by known option market prices. Unlike the classical inverse parabolic equation problem, the article transforms the original problem into an inverse problem with principal coefficients of the degenerate parabolic equation over a bounded region by variable substitution, thus avoiding the error introduced by artificial truncation. Under the optimal control framework, the problem is transformed into an optimization problem, the existence of the minimal solution is proved, and a mathematical proof of the convergence of the optimal solution is given. Finally, the gradient-type iterative method is applied to obtain the numerical solution of the inverse problem, and numerical experiments are conducted to verify it. This study provides an effective theoretical framework and numerical method for inferring the stock price drift rate from the option market price.

本文研究了基于退化抛物方程的期权定价逆漂移率问题的收敛性，旨在通过已知的期权市场价格恢复股票价格漂移率函数。与经典的反抛物方程问题不同，本文通过变量替换将原问题转化为退化抛物方程在有界区域上的主系数反问题，从而避免了人为截断带来的误差。在最优控制框架下，将该问题转化为优化问题，证明了最小解的存在性，并给出了最优解收敛性的数学证明。最后，采用梯度型迭代法得到了反问题的数值解，并进行了数值实验验证。本研究为从期权市场价格推断股票价格漂移率提供了有效的理论框架和数值方法。

引用次数: 0

A condition for the finite time blow up of the incompressible Navier–Stokes equations in the whole space 全空间不可压缩Navier-Stokes方程有限时间爆破的条件

IF 1.4 Q2 MATHEMATICS, APPLIED

Results in Applied Mathematics

Pub Date : 2025-05-01 DOI: 10.1016/j.rinam.2025.100590

Abdelhafid Younsi

This paper is interested in the existence of singularities for solutions of the Navier–Stokes equations in the whole space. We demonstrate the existence of initial data that leads to the unboundedness of the corresponding strong solution within a finite time. Our approach relies on lower and upper bounds of rates of decay for solutions to the Navier–Stokes equations. This result provides valuable insights into significant open problems in both physics and mathematics.

本文研究了Navier-Stokes方程解在整个空间中的奇异性。我们证明了初始数据的存在性，使得相应的强解在有限时间内无界。我们的方法依赖于Navier-Stokes方程解的衰减率的下界和上界。这一结果为物理学和数学中的重大开放问题提供了有价值的见解。

引用次数: 0

Study of nonlinear anisotropic elliptic problems with non-local boundary conditions in weighted variable exponent Sobolev spaces 加权变指数Sobolev空间中具有非局部边界条件的非线性各向异性椭圆问题的研究

IF 1.4 Q2 MATHEMATICS, APPLIED

Results in Applied Mathematics

Pub Date : 2025-05-01 DOI: 10.1016/j.rinam.2025.100597

Soumia EL OMARI, Said Melliani

This study investigates the existence of weak solutions for nonlinear anisotropic elliptic equations characterized by non-local boundary conditions within anisotropic weighted variable exponent Sobolev spaces. By employing variational methods and compact embedding theorems tailored to anisotropic Sobolev spaces, the research focuses on understanding the impact of anisotropy, non-locality, and weighted structures on the solution behavior. We establish sufficient conditions for the existence of solutions under various boundary conditions. These results deepen the understanding of anisotropic elliptic problems by highlighting the role of weighted structures and variable exponents in the interaction between anisotropy and non-locality. The study also explores non-local boundary conditions, which may include integrals of the unknown function over parts of the domain or non-local operators, often encountered in applications such as well modeling in 3D stratified petroleum reservoirs with arbitrary geometries. This work provides a solid theoretical foundation for broader applications in engineering and physics.

研究了各向异性加权变指数Sobolev空间中具有非局部边界条件的非线性各向异性椭圆方程弱解的存在性。利用各向异性Sobolev空间的变分方法和紧凑嵌入定理，重点研究了各向异性、非局域性和加权结构对解行为的影响。建立了在各种边界条件下解存在的充分条件。这些结果通过强调加权结构和变指数在各向异性和非局域性相互作用中的作用，加深了对各向异性椭圆问题的理解。该研究还探讨了非局部边界条件，其中可能包括部分区域上未知函数的积分或非局部算子，这些情况在任意几何形状的三维分层油藏的井建模等应用中经常遇到。这项工作为工程和物理的广泛应用提供了坚实的理论基础。

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引用次数: 0

The regression-based efficient frontier 基于回归的效率边界

IF 1.4 Q2 MATHEMATICS, APPLIED

Results in Applied Mathematics

Pub Date : 2025-05-01 DOI: 10.1016/j.rinam.2025.100578

Wan-Yi Chiu

The standard mean–variance analysis employs quadratic optimization to determine the optimal portfolio weights and to plot the mean–variance efficient frontier (MVEF). It then indirectly evaluates the mean–variance efficiency test (MVET) by considering the maximum Sharpe ratios of the tangency portfolio within the MVEF framework, which assumes a risk-free rate. This paper integrates these procedures without considering the risk-free rate by transitioning to a regression-based efficient frontier (RBEF). The RBEF estimates the optimal portfolio weights and simultaneously implements the MVET based on an OLS F-test, offering a simpler approach to portfolio optimization.

标准均值-方差分析采用二次优化方法确定最优投资组合权重，并绘制均值-方差有效边界。然后，通过考虑MVEF框架内切线投资组合的最大夏普比率（假设无风险利率），间接评估均值方差效率检验（MVET）。本文通过过渡到基于回归的有效边界（RBEF）来整合这些过程，而不考虑无风险率。RBEF估计了最优投资组合权重，同时基于OLS f检验实现了MVET，为投资组合优化提供了一种更简单的方法。

引用次数: 0

An arbitrary-order Virtual Element Method for the Helmholtz equation applied to wave field calculation in port 赫姆霍兹方程的任意阶虚元法在港口波场计算中的应用

IF 1.4 Q2 MATHEMATICS, APPLIED

Results in Applied Mathematics

Pub Date : 2025-05-01 DOI: 10.1016/j.rinam.2025.100598

Ronan Dupont

The Virtual Element Method (VEM), as a high-order polytopal method, offers significant advantages over traditional Finite Element Methods (FEM). In particular, it allows the handling of polytopal or non-conforming meshes which greatly simplificates the mesh generation procedure. In this paper, the VEM is used for the discretization of the Helmholtz equations with a Robin-type absorbing boundary condition. This problem is crucial in various fields, including coastal engineering, oceanography and the design of offshore structures. Details of the VEM implementation with Robin boundary condition are given. Numerical results on test cases with analytical solutions show that the methods can provide optimal convergence rates for smooth solutions. Then, as a more realistic test case, the computation of the eigenmodes of the port of Cherbourg is carried out.

虚拟元法（VEM）作为一种高阶多面体方法，具有传统有限元法（FEM）无法比拟的优势。特别是，它允许处理多边形或不一致的网格，大大简化了网格生成过程。本文将向量机用于具有robin型吸收边界条件的亥姆霍兹方程的离散化。这个问题在许多领域都是至关重要的，包括海岸工程、海洋学和近海结构物的设计。给出了基于Robin边界条件的VEM的具体实现方法。具有解析解的测试用例的数值结果表明，该方法能够提供最优的光滑解收敛速率。然后，作为一个更实际的试验案例，对瑟堡港的本征模态进行了计算。

引用次数: 0

Fast numerical algorithms for solving opposite-bordered tridiagonal Toeplitz linear systems and their applications 求解对边三对角Toeplitz线性系统的快速数值算法及其应用

IF 1.4 Q2 MATHEMATICS, APPLIED

Results in Applied Mathematics

Pub Date : 2025-05-01 DOI: 10.1016/j.rinam.2025.100581

Hcini Fahd

This paper presents two fast numerical algorithms for solving opposite-bordered tridiagonal Toeplitz linear systems. Both algorithms are designed to solve a system of

n

equations in linear time. The first algorithm uses a block

2 \times 2

-LU factorization combined with a fast approach for solving upper quasi-triangular Toeplitz systems. The second algorithm applies a splitting technique to the opposite-bordered tridiagonal Toeplitz matrix, along with a fast algorithm for solving tridiagonal Toeplitz systems. The effectiveness of the proposed algorithms is demonstrated through numerical experiments.

本文给出了求解对边三对角Toeplitz线性方程组的两种快速数值算法。这两种算法都设计用于在线性时间内求解n个方程的系统。第一种算法使用块2×2-LU分解与快速求解上拟三角形Toeplitz系统的方法相结合。第二种算法将分割技术应用于对边三对角Toeplitz矩阵，以及求解三对角Toeplitz系统的快速算法。通过数值实验验证了算法的有效性。

引用次数: 0

A generalized smoothed particle hydrodynamics method based on the moving least squares method and its discretization error estimation 基于移动最小二乘法的广义光滑质点流体力学方法及其离散化误差估计

IF 1.4 Q2 MATHEMATICS, APPLIED

Results in Applied Mathematics

Pub Date : 2025-05-01 DOI: 10.1016/j.rinam.2025.100594

Kensuke Shobuzako , Shigeo Yoshida , Yoshifumi Kawada , Ryosuke Nakashima , Shujiro Fujioka , Mitsuteru Asai

This paper demonstrates that the least squares method can generalize conventional discretized models of the smoothed particle hydrodynamics (SPH) method and proposes a simple discretization error evaluation for the SPH method, which is based on the truncation error of the least squares method. Since classical SPH models are formulated under the ideal assumption of a uniform particle distribution, their accuracies deteriorate to zeroth order or worse when the particle configuration is disordered. Although numerous advanced SPH models have been developed that ensure the spatial discretization accuracies of first order or higher under non-ideal conditions, their similarities and differences remain unexplored. This has motivated us to construct a generalized formulation encompassing existing SPH models. Almost all of the classical SPH and the advanced SPH models can be mathematically unified by the generalized particle method based on the least squares fitting, namely, the moving least squares (MLS) method. By deriving its truncation error, we analytically evaluate and numerically verify the discretization errors of various SPH models. These results confirm that all the classical SPH models exhibit zeroth-order or “negative” first-order accuracy, whose error increases as the particle spacing decreases. This paper proposes a generalized SPH model based on the MLS scheme with arbitrary accuracy for spatial derivatives of any order. This model is referred to as the least squares SPH (LSSPH) model. Additionally, we perform some benchmark tests to validate the LSSPH model with second-order accuracy for the zeroth and the first derivatives and first-order accuracy for the second derivatives.

本文论证了最小二乘法可以推广光滑颗粒流体动力学（SPH）方法的传统离散化模型，并提出了基于最小二乘法截断误差的SPH方法的简单离散化误差评价方法。由于经典SPH模型是在粒子均匀分布的理想假设下建立的，当粒子构型无序时，其精度会下降到零阶甚至更低。虽然已经开发了许多先进的SPH模型，以确保在非理想条件下的一阶或更高的空间离散精度，但它们的异同仍未被探索。这促使我们构建一个包含现有SPH模型的广义公式。基于最小二乘拟合的广义粒子方法，即移动最小二乘（MLS）方法，几乎可以将所有的经典SPH模型和先进SPH模型在数学上统一起来。通过推导其截断误差，对各种SPH模型的离散化误差进行了分析评价和数值验证。这些结果证实了所有经典SPH模型都具有零阶或“负”一阶精度，其误差随着粒子间距的减小而增大。针对任意阶空间导数，提出了一种基于任意精度MLS格式的广义SPH模型。该模型称为最小二乘SPH （LSSPH）模型。此外，我们执行了一些基准测试，以验证LSSPH模型的零阶导数和一阶导数的二阶精度以及二阶导数的一阶精度。

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引用次数: 0

Jump amplitude inference in SDEs with cosine kernel 带余弦核的SDEs跳幅推断

IF 1.4 Q2 MATHEMATICS, APPLIED

Results in Applied Mathematics

Pub Date : 2025-05-01 DOI: 10.1016/j.rinam.2025.100596

Wuchen Li , Luwen Zhang , Jian Xu , Linghui Li , Liping Bai

For estimating the jump amplitude in stochastic differential equations with jumps, existing parameter estimation methods in the academic community suffer from inherent systematic errors. Commonly used kernel functions often assume symmetric distributions, limiting their ability to model skewed distributions. Many methods can simulate positively skewed distributions but fail to handle negatively skewed ones, and they tend to overestimate the probability density when the jump size is close to zero. This paper introduces a novel kernel density estimation method based on cosine functions for jump amplitude estimation. Our approach addresses these systematic errors, especially under large sample conditions, enabling more accurate statistical inference for the jump amplitude in stochastic differential equations with jumps. We anticipate that this method will contribute positively to research in areas such as finance and signal processing.

对于具有跳变的随机微分方程的跳变幅度估计，学术界现有的参数估计方法存在固有的系统误差。常用的核函数通常假设对称分布，限制了它们对倾斜分布建模的能力。许多方法可以模拟正偏态分布，但不能处理负偏态分布，而且当跳跃大小接近于零时，它们往往会高估概率密度。提出了一种基于余弦函数的核密度估计方法，用于跳幅估计。我们的方法解决了这些系统误差，特别是在大样本条件下，能够对具有跳跃的随机微分方程的跳跃幅度进行更准确的统计推断。我们预计这种方法将对金融和信号处理等领域的研究做出积极贡献。

引用次数: 0

Modeling prebunking strategies to contain misinformation spread 建模预掩体策略，以遏制错误信息的传播

IF 1.4 Q2 MATHEMATICS, APPLIED

Results in Applied Mathematics

Pub Date : 2025-05-01 DOI: 10.1016/j.rinam.2025.100591

Giorgio Martalò , Marco Menale , Romina Travaglini

We propose a first model describing the impact of prebunking strategies on misinformation dynamics. Following a classical epidemiological approach, the population is structured into interacting functional subsystems, representing individuals with different susceptibility levels. Transitions between subsystems occur with fixed probabilities, while the prebunking strategy is modeled as an external action. A reduced system of equations is derived, and the stability analysis is performed to investigate the effectiveness of the prebunking strategy. Numerical simulations confirm the benefits of interventions in mitigating the spread of fake news, providing insights into digital misinformation dynamics.

我们提出了第一个模型来描述预掩体策略对错误信息动态的影响。根据经典的流行病学方法，将人群划分为相互作用的功能子系统，代表不同易感水平的个体。子系统之间的转换以固定的概率发生，而预掩体策略被建模为外部行为。导出了简化方程组，并进行了稳定性分析，验证了预加料策略的有效性。数值模拟证实了干预措施在缓解假新闻传播方面的好处，提供了对数字错误信息动态的洞察。

引用次数: 0

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