Journal of Computational and Applied Mathematics最新文献

英文中文

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 : 2026-01-17 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

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 : 2026-01-16 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

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 : 2026-01-16 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

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 : 2026-01-16 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

Robust divergence-based tests of hypotheses for simple step-stress accelerated life-testing under Gamma lifetime distributions 伽玛寿命分布下简单阶跃应力加速寿命试验假设的稳健发散检验

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2026-01-13 DOI: 10.1016/j.cam.2026.117362

Narayanaswamy Balakrishnan , María Jaenada , Leandro Pardo

Many modern devices are highly reliable, with long lifetimes before their failure. Conducting reliability tests under actual use conditions may require therefore impractically long experimental times to gather sufficient data for developing accurate inference. To address this, Accelerated Life Tests (ALTs) are often used in industrial experiments to induce product degradation and eventual failure more quickly by increasing certain environmental stress factors. Data collected under such increased stress conditions are analyzed, and results are then extrapolated to normal operating conditions. These tests typically involve a small number of devices and so pose significant challenges, such as interval-censoring. As a result, the outcomes are particularly sensitive to outliers in the data. Additionally, a comprehensive analysis requires more than just point estimation; inferential methods such as confidence intervals and hypothesis testing are essential to fully assess the reliability behaviour of the product.

This paper presents robust statistical methods based on minimum divergence estimators for analyzing ALT data of highly reliable devices under step-stress conditions and Gamma lifetime distributions. Robust test statistics generalizing the Rao test and divergence-based tests for testing linear null hypothesis are then developed. These hypotheses include in particular tests for the significance of the identified stress factors and for the validity of the assumption of exponential lifetimes.

许多现代设备非常可靠，故障前寿命很长。因此，在实际使用条件下进行可靠性测试可能需要很长的实验时间来收集足够的数据以进行准确的推断。为了解决这个问题，工业实验中经常使用加速寿命试验（ALTs），通过增加某些环境应力因素来更快地诱导产品降解并最终失效。在这种增加的应力条件下收集的数据进行分析，然后将结果外推到正常的操作条件。这些测试通常涉及少量设备，因此带来了重大挑战，例如间隔审查。因此，结果对数据中的异常值特别敏感。此外，全面分析需要的不仅仅是点估计；推断方法，如置信区间和假设检验是必要的，以充分评估产品的可靠性行为。本文提出了一种基于最小散度估计的鲁棒统计方法，用于分析阶跃应力条件下高可靠器件的ALT数据和Gamma寿命分布。鲁棒检验统计推广Rao检验和基于散度的检验线性零假设，然后发展。这些假设特别包括对已确定的压力因素的重要性和指数寿命假设的有效性的检验。

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引用次数: 0

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 : 2026-01-13 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

A quadratic approximation for solving nonlinear integral equations of Volterra type 求解非线性Volterra型积分方程的二次逼近

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2026-01-13 DOI: 10.1016/j.cam.2026.117366

J.~A. Ezquerro, M.~A. Hernández-Verón

By using fixed point techniques, we analyze the existence and location of solution of a nonlinear integral equation of Volterra type. These techniques are used to approximate solutions to integral equations of this type, which also allow us to approximate them with quadratic convergence. Besides, we improve this analysis by applying collocation methods based on interpolation polynomials of Lagrange that use zeros of orthogonal Chebyshev polynomials as collocation points. In addition, to solve the sensitivity and ill-conditioning problems that might arise, we apply an Ulm-type iterative method that does not use inverses in the algorithm, but only matrix products.

利用不动点技术，分析了一类非线性Volterra型积分方程解的存在性和位置。这些技巧被用来近似这类积分方程的解，这也允许我们用二次收敛来近似它们。此外，我们采用基于拉格朗日插值多项式的配点方法，以正交切比雪夫多项式的零点为配点，改进了这一分析。此外，为了解决可能出现的敏感性和病态问题，我们采用了ulm型迭代方法，该方法在算法中不使用逆，而只使用矩阵积。

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 : 2026-01-13 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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引用次数: 0

Adaptive fractional-order primal-dual image denoising algorithm based on Lq quasi-norm 基于Lq准范数的自适应分数阶原对偶图像去噪算法

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2026-01-12 DOI: 10.1016/j.cam.2026.117352

Shaojiu Bi , Minmin Li , Guangcheng Cai

This study proposes a nonconvex fractional-order variational model for Gaussian noise removal, and a corresponding solution method is designed based on the primal-dual algorithm. Due to the significant advantages of combining the nonconvex L_q quasi-norm and the fractional-order total variation, the proposed model can better suppress the staircase effect, thereby improving the quality of the recovered image. An adaptive regularization parameter is designed based on the Morozov discrepancy principle to ensure the denoised image remains in a particular set. The algorithm’s convergence is analyzed using various mathematical theories, such as sampling saddle point theory. Simulation and comparison experiments verify the effectiveness of the algorithm in image denoising.

提出了高斯噪声去除的非凸分数阶变分模型，并基于原对偶算法设计了相应的求解方法。由于将非凸Lq准范数与分数阶总变分相结合的显著优势，该模型可以更好地抑制阶梯效应，从而提高恢复图像的质量。基于Morozov差异原理设计自适应正则化参数，保证去噪后的图像保持在特定的集合中。利用采样鞍点理论等数学理论分析了该算法的收敛性。仿真和对比实验验证了该算法对图像去噪的有效性。

引用次数: 0

Efficient preconditioning techniques for time-fractional PDE-constrained optimization problems 时间分数阶pde约束优化问题的有效预处理技术

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2026-01-11 DOI: 10.1016/j.cam.2026.117348

Zhao-Zheng Liang , Guo-Feng Zhang , Lei Zhang , Mu-Zheng Zhu

In this paper, we develop efficient preconditioning techniques for distributed optimal control problems governed by partial differential equations with Caputo fractional derivative in time. By employing a discretize-then-optimize approach combining mixed all-at-once schemes of finite-difference for temporal and finite-element for spatial discretizations, we derive a large-scale and ill-conditioned Kronecker structured block two-by-two linear system with distinct pivot blocks. A block approximate factorization preconditioning method that is well-suited for approximating the Schur complement is considered by utilizing the so called matching strategy. A distinctive feature of the proposed preconditioner is its computational efficiency arising from its practical Schur complement-free implementation manner. Furthermore, the eigenvalues of the preconditioned system are demonstrated to lie within parameter-free positive real intervals, ensuring fast convergence independent of problem parameters under Krylov subspace acceleration. Motivated by the inherent block-Toeplitz structures, circulant-based inexact variants of the proposed preconditioner are explored and implemented within diagonalization strategies by fast Fourier transformation (FFT). Numerical experiments are conducted to validate the effectiveness and robustness of our proposed preconditioners compared with some optimal preconditioning strategies.

本文研究了具有Caputo分数阶导数的偏微分方程的分布最优控制问题的有效预处理技术。采用一种先离散后优化的方法，结合时间有限差分和空间有限单元的混合一次性格式，我们得到了一个具有不同支点块的大型病态Kronecker结构块二乘二线性系统。利用所谓的匹配策略，考虑了一种适合于近似舒尔补的块近似分解预处理方法。所提出的前置条件的一个显著特征是其计算效率源于其实际的舒尔互补实现方式。进一步证明了预条件系统的特征值位于无参数的正实区间内，保证了在Krylov子空间加速下与问题参数无关的快速收敛。在固有块toeplitz结构的驱动下，通过快速傅立叶变换（FFT）在对角化策略中探索并实现了所提出的预条件的基于循环的不精确变体。通过数值实验验证了所提预处理策略与一些最优预处理策略的有效性和鲁棒性。

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