Journal of Computational and Applied Mathematics最新文献

英文中文

AI-augmented fractional-order modeling and control of chaotic systems: A physics-informed neural approach 人工智能增强的分数阶建模和混沌系统控制：一种物理信息神经方法

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2026-09-01 Epub Date: 2026-01-13 DOI: 10.1016/j.cam.2026.117335

Paul Ndy Von Kluge , G.G. Sengha , B. Doumia

This paper presents an enhanced hybrid modeling and control framework for nonlinear chaotic systems, integrating fractional-order dynamics with deep learning techniques. A novel Physics-Informed Neural Network (PINN) architecture is developed to learn, approximate, and control the behavior of complex fractional-order systems without requiring explicit knowledge of their governing equations. Beyond traditional fixed-order settings, the framework is extended to accommodate variable-order and multi-dimensional fractional systems, enabling more accurate modeling of memory-dependent processes found in real-world applications. The method is applied to canonical chaotic systems including fractional-order Lorenz and Chen models, extended to multi-dimensional cases and further generalized to robust control scenarios under external disturbances and parametric uncertainties. Simulation results confirm the framework’s ability to reconstruct system trajectories with high fidelity, synthesize stable control policies, and achieve data-efficient learning from sparse observations. These advancements strengthen the scalability, adaptability to sudden parameter variations, and theoretical robustness of the proposed approach, making it well-suited for applications in chaotic, biological, fractional PID control, and other complex engineering systems.

本文提出了一种增强的非线性混沌系统混合建模和控制框架，将分数阶动力学与深度学习技术相结合。开发了一种新的物理信息神经网络（PINN）架构，用于学习，近似和控制复杂分数阶系统的行为，而无需明确了解其控制方程。除了传统的固定顺序设置之外，该框架还扩展到适应可变顺序和多维分数系统，从而能够更准确地建模现实应用程序中发现的依赖内存的进程。该方法应用于正则混沌系统，包括分数阶Lorenz和Chen模型，扩展到多维情况，并进一步推广到外部干扰和参数不确定性下的鲁棒控制场景。仿真结果证实了该框架能够高保真地重建系统轨迹，合成稳定的控制策略，并从稀疏观测中实现数据高效学习。这些进步加强了所提出方法的可扩展性、对突然参数变化的适应性和理论鲁棒性，使其非常适合于混沌、生物、分数PID控制和其他复杂工程系统的应用。

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引用次数: 0

Investigating numerical solutions and ensuring stability in nonlinear pseudo hyperbolic telegraph equations 研究非线性伪双曲电报方程的数值解与稳定性

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2026-09-01 Epub Date: 2026-01-16 DOI: 10.1016/j.cam.2026.117371

Praveen Agarwal , Mahmut Modanli , Hazal Yüksekkaya , Sadeq Taha Abdulazeez , Shilpi Jain

This research explores the application of an explicit finite difference scheme to solve the nonlinear pseudo-hyperbolic telegraph equation (NPHTE). We develop a novel first-order difference approach tailored to this complex problem. Utilising MATLAB, we implement the explicit finite difference scheme to obtain approximate numerical solutions. Our study demonstrates the stability of this difference scheme for the NPHTE through rigorous mathematical proof. To evaluate the accuracy of our method, we conduct a comparative analysis between analytical and numerical solutions, quantifying the associated errors. We present graphical representations of the solutions to enhance understanding of the problem's behavior. Furthermore, we provide comprehensive simulation results for the NPHTE using our approach, including visual representations and error assessments. This thorough investigation and validation of our methodology significantly contribute to the understanding and application of the NPHTE in mathematical modeling and simulation across various scientific and engineering domains.

研究了用显式有限差分格式求解非线性伪双曲电报方程的方法。针对这一复杂问题，我们提出了一种新颖的一阶差分方法。利用MATLAB实现了显式有限差分格式，得到近似数值解。我们的研究通过严格的数学证明证明了这种差分格式对于NPHTE的稳定性。为了评估我们方法的准确性，我们对解析解和数值解进行了比较分析，量化了相关误差。我们给出了解决方案的图形表示，以增强对问题行为的理解。此外，我们使用我们的方法提供了NPHTE的综合仿真结果，包括视觉表示和误差评估。对我们方法的深入调查和验证，极大地促进了NPHTE在各种科学和工程领域的数学建模和仿真中的理解和应用。

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引用次数: 0

Exact variance of the associated Rician phase distribution 相关相位分布的精确方差

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2026-09-01 Epub Date: 2026-01-16 DOI: 10.1016/j.cam.2026.117337

Jolyon M. De Freitas

The Rician phase distribution has been used in many scientific and engineering disciplines to model the phase noise of a vector driven by additive Gaussian noise. It appears that no exact closed-form expression exists in the open literature for the variance of this phase distribution. This paper offers a new exact closed-form expression for the variance of the Rician phase distribution in terms of incomplete hypergeometric

_{3} F_{1}

functions. The Rician phase variance is compared to the second circular moments of the von Mises and wrapped Normal distributions showing that when the interpretations of the variances are ignored, all are compatible if the input signal-to-noise ratios are very large. This also leads to a new way in summing the Fourier expansion terms of the Rician phase distribution. In general, the incomplete hypergeometric functions

_{p + 2} F_{p}, p = 0, 1, 2, \dots

are shown to be conditionally convergent.

在许多科学和工程学科中，已经使用了相位分布来模拟由加性高斯噪声驱动的矢量的相位噪声。在公开文献中，似乎不存在这种相位分布方差的精确封闭表达式。本文用不完全超几何3F1函数给出了一种新的精确闭式表示。将其相位方差与von Mises和包装正态分布的第二个圆矩进行比较，表明当忽略方差的解释时，如果输入信噪比非常大，则所有方差都是兼容的。这也导致了一种新的方法来求和的傅里叶展开项的相位分布。一般来说，不完全超几何函数p+2Fp，p=0,1,2，⋯被证明是有条件收敛的。

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引用次数: 0

Spline quasi-interpolating and quasi2-interpolating projectors for the numerical solution of Cauchy singular integral equations 柯西奇异积分方程数值解的样条拟插值和拟2插值投影

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2026-09-01 Epub Date: 2026-01-21 DOI: 10.1016/j.cam.2026.117376

Alessandra Aimi , Mattia Alex Leoni , Sara Remogna

The paper deals with the numerical solution of Cauchy singular integral equations, by means of spline quasi interpolating projectors and their variant quasi²-interpolating projectors, within a collocation approach which takes into account the particular features of the problem at hand. Several numerical results, including those related to the application of the presented approach to an extended model problem, validate the proposed error estimates.

本文利用样条拟插值投影和它们的变型拟2-插值投影，考虑到问题的特殊性，用配点法研究了柯西奇异积分方程的数值解。几个数值结果，包括与所提出的方法应用于扩展模型问题有关的结果，验证了所提出的误差估计。

引用次数: 0

Efficient stability-preserving schemes for stochastic McKean-Vlasov equations with uncertainty 不确定性随机McKean-Vlasov方程的高效保稳方案

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2026-09-01 Epub Date: 2026-01-17 DOI: 10.1016/j.cam.2026.117361

Haiyan Yuan , Quanxin Zhu

In this paper, we address the stability analysis of stochastic McKean-Vlasov equations with uncertainty (more specifically, stochastic McKean-Vlasov equations driven by G-Brownian motion, G-SMVEs for short) in the absence of Lyapunov functions. Uncertainty probability and distribution dependence prevent us from directly applying the techniques for investigating the stability of stochastic differential equations and stochastic McKean-Vlasov equations to G-SMVEs. To overcome this difficulty, with the help of the G-expectation theory, we use the empirical mean to approximate the law which is defined via the G-expectation, and then construct interacting particle systems to approximate G-SMVEs. We prove that there is a stability equivalence between a G-SMVE and the associated interacting particle system. We also show that the mean square exponential stability of the interacting particle system is equivalent to that of the stochastic theta method, which enables us to investigate the stability of G-SMVEs by carrying out careful numerical simulations. Moreover, the mean square exponential stability of the interacting particle system (or its stochastic theta method) implies the quasi sure exponential stability, but the converse may not be true unless imposing further requirements. Finally, we provide one example to verify our theoretical results.

本文研究了不确定性随机McKean-Vlasov方程（更具体地说，是由g - brown运动驱动的随机McKean-Vlasov方程，简称G-SMVEs）在没有Lyapunov函数的情况下的稳定性分析。不确定性、概率和分布依赖性使我们无法将随机微分方程和随机McKean-Vlasov方程的稳定性研究技术直接应用于g - smv。为了克服这一困难，我们借助g -期望理论，利用经验均值逼近由g -期望定义的定律，然后构造相互作用的粒子系统来逼近g - smve。我们证明了G-SMVE与相关的相互作用粒子系统之间存在稳定性等价。我们还证明了相互作用粒子系统的均方指数稳定性与随机θ方法的均方指数稳定性等效，这使我们能够通过进行仔细的数值模拟来研究G-SMVEs的稳定性。此外，相互作用粒子系统的均方指数稳定性（或其随机θ方法）意味着准确定的指数稳定性，但除非施加进一步的要求，否则反之可能不成立。最后，给出一个算例来验证我们的理论结果。

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引用次数: 0

Double inertial contraction method for monotone inclusion problems for medical image recovery and data classifications 医学图像恢复和数据分类中单调包含问题的双惯性收缩方法

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2026-09-01 Epub Date: 2026-01-16 DOI: 10.1016/j.cam.2026.117369

Pongsakorn Sunthrayuth , Prasit Cholamjiak , Issara Siramaneerat , Jen-Chih Yao

In this paper, we propose an inertial contraction method incorporating two sequences of inertial parameters to solve monotone inclusion problems in real Hilbert spaces. The method employs a self-adaptive technique that enables automatic updating of key parameters throughout the iterative process. We establish weak, strong, and R-linear convergence of the proposed algorithm under suitable parameter conditions. In addition, numerical experiments on image restoration and data classification are provided to demonstrate the effectiveness and practical relevance of the method.

本文提出了一种包含两个惯性参数序列的惯性收缩方法来解决实数Hilbert空间中的单调包含问题。该方法采用了一种自适应技术，能够在整个迭代过程中自动更新关键参数。在适当的参数条件下，证明了算法的弱收敛性、强收敛性和r -线性收敛性。通过图像恢复和数据分类的数值实验，验证了该方法的有效性和实用性。

引用次数: 0

An efficient matrix free optimization algorithm combining a revised PRP and FR-CG type methods with application to robotics 结合改进的PRP和FR-CG型方法的一种有效的无矩阵优化算法及其在机器人中的应用

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2026-09-01 Epub Date: 2026-01-23 DOI: 10.1016/j.cam.2026.117378

Nasiru Salihu , Poom Kumam , Aliyu Muhammed Awwal , Mathew Remilekun Odekunle , Thidaporn Seangwattana

Many problems arise from science and engineering which can be expressed as an unconstrained minimization problem. Therefore, developing numerical methods to obtain their approximate solutions has become necessary, as their exact solutions cannot be obtained. Several such numerical methods have been proposed, with the conjugate gradient (CG) method stands out to be more efficient in handling this type of problem, due to its nice theoretical structure and promising numerical result. In this article, we consider a CG algorithm based on a generalized conjugacy condition. The new CG parameter is selected to ensure a convex combination of modified version of the Polak, Ribière-Polyak (PRP) and Fletcher-Revees (FR) CG algorithms. The numerical implementation adopts inexact line search which revealed that the scheme is robust when compared with some known efficient algorithms in literature. Furthermore, the theoretical analysis shows that the proposed method converge globally. The method is also applicable to solve three degree of freedom motion control robotic model.

科学和工程中出现的许多问题都可以表示为无约束最小化问题。因此，发展数值方法来获得它们的近似解是必要的，因为它们的精确解不能得到。目前已经提出了几种这样的数值方法，其中共轭梯度法（CG）由于其良好的理论结构和令人满意的数值结果，在处理这类问题时更为有效。在本文中，我们考虑了一种基于广义共轭条件的CG算法。选择新的CG参数是为了确保Polak、ribire - polyak （PRP）和Fletcher-Revees (FR) CG算法的改进版本的凸组合。数值实现采用非精确直线搜索，与文献中已知的一些高效算法相比，该算法具有较强的鲁棒性。理论分析表明，该方法具有全局收敛性。该方法同样适用于求解三自由度运动控制机器人模型。

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引用次数: 0

Novel Birkhoff-hermite ERKN methods for solving general second-order highly oscillatory systems 求解一般二阶高振荡系统的Birkhoff-hermite ERKN新方法

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2026-09-01 Epub Date: 2026-01-21 DOI: 10.1016/j.cam.2026.117375

Yonglei Fang , Changying Liu , Xiong You

This paper is devoted to the effective integration of general second-order highly oscillatory systems. By approximating the nonlinear integrals appeared in the matrix-variation-of-constants formula with the Birkhoff-Hermite interpolating polynomial, new ERKN integrators (BHERKN) are obtained. The symmetry and nonlinear stability of the BHERKN integrators are analyzed. By energy analysis, the BHERKN integrators are shown to converge with an arbitrary high-order. Finally, numerical experiments are reported to show the high efficiency, accuracy and robustness of our new methods.

研究一般二阶高振荡系统的有效积分问题。用Birkhoff-Hermite插值多项式逼近矩阵-常数变分公式中的非线性积分，得到新的ERKN积分器（BHERKN）。分析了BHERKN积分器的对称性和非线性稳定性。通过能量分析，证明了BHERKN积分器具有任意高阶收敛性。最后，通过数值实验验证了该方法的有效性、准确性和鲁棒性。

引用次数: 0

Fröbenius expansions for second-order random differential equations: Stochastic analysis and applications to Lindley-type damping models Fröbenius二阶随机微分方程的展开式：随机分析和林德利型阻尼模型的应用

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2026-09-01 Epub Date: 2026-01-22 DOI: 10.1016/j.cam.2026.117379

Halim Zeghdoudi , Mohamed Amine Kerker , Elif Boduroglu

This paper develops a Frobenius series framework for the stochastic analysis of second–order random differential equations of the form

\ddot{Y} (t) + A (t) \dot{Y} (t) = 0,

where the damping coefficient A(t) is a positive stochastic process and the initial conditions are square–integrable random variables. Assuming mean–square analyticity of A(t) in a neighborhood of the initial time, we establish existence and uniqueness of the solution in L²(Ω) and derive exponentially convergent truncation error bounds for the associated Frobenius expansion. The resulting series representation enables the numerical approximation of the probability density function of Y(t) via Monte Carlo simulation. To improve computational efficiency, a control variates strategy is incorporated for variance reduction.

A comprehensive numerical study is conducted for a broad family of positive, right–skewed damping distributions, including the Lindley, XLindley, New XLindley (NXLD), Gamma–Lindley, Inverse–Lindley, Truncated–Lindley, Log–Lindley, and a newly proposed Mixed Lindley–Uniform model. The simulations illustrate how different tail behaviors and boundedness properties of the damping coefficient influence the stochastic dynamics and the accuracy of density estimation. Finally, stylized applications to option pricing and Value–at–Risk estimation are presented to illustrate how the Frobenius–based framework and control variates methodology can be embedded within standard uncertainty quantification workflows. Overall, the proposed approach provides a flexible and computationally efficient tool for the analysis of randomly damped dynamical systems.

本文建立了一类二阶随机微分方程(my¨(t)+ a （t)Y˙(t)=0）随机分析的Frobenius级数框架，其中阻尼系数a (t)是一个正随机过程，初始条件是平方可积随机变量。假设A(t)在初始时间的邻域具有均方分析性，我们建立了该解在L2（Ω）上的存在唯一性，并推导出相应的Frobenius展开式的指数收敛截断误差界。所得到的序列表示可以通过蒙特卡罗模拟对Y(t)的概率密度函数进行数值逼近。为了提高计算效率，采用控制变量策略减小方差。本文对一系列正的、右偏的阻尼分布进行了全面的数值研究，包括Lindley、XLindley、New XLindley （NXLD）、Gamma-Lindley、Inverse-Lindley、trunted - Lindley、Log-Lindley以及新提出的Mixed Lindley - uniform模型。仿真结果说明了阻尼系数的不同尾态和有界性对随机动力学和密度估计精度的影响。最后，介绍了期权定价和风险价值估计的程式化应用，以说明如何将基于frobenius的框架和控制变量方法嵌入到标准的不确定性量化工作流程中。总的来说，所提出的方法为随机阻尼动力系统的分析提供了一种灵活且计算效率高的工具。

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引用次数: 0

Optimizing liquidity provision in Uniswap v3 via physics-informed neural networks 通过物理信息神经网络优化Uniswap v3的流动性供应

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2026-09-01 Epub Date: 2026-01-13 DOI: 10.1016/j.cam.2026.117368

Salvatore Cuomo , Federico Gatta , Vincenzo Vocca

Decentralized Exchanges are rapidly changing financial markets by using blockchain technology to eliminate intermediaries. Among others, Uniswap v3 is the most prominent due to the Concentrated Liquidity mechanism, which allows liquidity providers to allocate capital within flexible price ranges, thus increasing possible revenues. This feature brings a key trade-off: narrower ranges increase both potential returns and the risk of inactive liquidity; wider ranges ensure continuous but lower profits. Thus, developing approaches for choosing the optimal liquidity provision range is becoming a predominant task both in the industry and academia. In this work, we propose a novel framework for optimizing liquidity provision in Uniswap v3 using Physics-Informed Neural Networks (PINNs). Our approach models market dynamics through stochastic processes and employs the Feynman-Kac theorem to compute the expected utility associated with the provision position as the solution of a Partial Differential Equation (PDE). This PDE is then solved using PINNs, enabling a fast approximation of expected utility. In such a way, it is possible to efficiently optimize the liquidity allocation in real-time with minimal computational cost. We assess our methodology through numerical experiments, where the backtesting results over eight pools demonstrate its effectiveness in optimizing liquidity provision performance. Thus, our results highlight the potential of the proposed framework for real-world applications.

通过使用区块链技术消除中介机构，去中心化交易所正在迅速改变金融市场。其中，Uniswap v3是最突出的，因为它的集中流动性机制，允许流动性提供者在灵活的价格范围内分配资本，从而增加可能的收入。这一特征带来了一个关键的权衡：较窄的波动幅度既增加了潜在回报，也增加了流动性不活跃的风险；较宽的范围确保了持续但较低的利润。因此，研究选择最优流动性供给区间的方法已成为业界和学术界的主要课题。在这项工作中，我们提出了一个使用物理信息神经网络（pinn）优化Uniswap v3流动性供应的新框架。我们的方法通过随机过程对市场动态进行建模，并采用费曼-卡茨定理来计算与供应位置相关的期望效用，作为偏微分方程（PDE）的解。然后使用pin来解决该PDE，从而实现对预期效用的快速近似。这样，就有可能以最小的计算成本实时有效地优化流动性分配。我们通过数值实验来评估我们的方法，其中八个池的回测结果证明了其在优化流动性提供性能方面的有效性。因此，我们的结果突出了所提出的框架在实际应用中的潜力。

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