Journal of Computational and Applied Mathematics最新文献

{"title":"AI-augmented fractional-order modeling and control of chaotic systems: A physics-informed neural approach","authors":"Paul Ndy Von Kluge ,&nbsp;G.G. Sengha ,&nbsp;B. Doumia","doi":"10.1016/j.cam.2026.117335","DOIUrl":"10.1016/j.cam.2026.117335","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"483 ","pages":"Article 117335"},"PeriodicalIF":2.6,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146039552","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Investigating numerical solutions and ensuring stability in nonlinear pseudo hyperbolic telegraph equations","authors":"Praveen Agarwal ,&nbsp;Mahmut Modanli ,&nbsp;Hazal Yüksekkaya ,&nbsp;Sadeq Taha Abdulazeez ,&nbsp;Shilpi Jain","doi":"10.1016/j.cam.2026.117371","DOIUrl":"10.1016/j.cam.2026.117371","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"483 ","pages":"Article 117371"},"PeriodicalIF":2.6,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146039579","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Exact variance of the associated Rician phase distribution","authors":"Jolyon M. De Freitas","doi":"10.1016/j.cam.2026.117337","DOIUrl":"10.1016/j.cam.2026.117337","url":null,"abstract":"<div><div>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 <span><math><mrow><msub><mrow></mrow><mn>3</mn></msub><msub><mi>F</mi><mn>1</mn></msub></mrow></math></span> 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 <span><math><mrow><msub><mrow></mrow><mrow><mi>p</mi><mo>+</mo><mn>2</mn></mrow></msub><msub><mi>F</mi><mi>p</mi></msub><mo>,</mo><mspace></mspace><mspace></mspace><mi>p</mi><mo>=</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>⋯</mo></mrow></math></span> are shown to be conditionally convergent.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"483 ","pages":"Article 117337"},"PeriodicalIF":2.6,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146039553","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Spline quasi-interpolating and quasi2-interpolating projectors for the numerical solution of Cauchy singular integral equations","authors":"Alessandra Aimi ,&nbsp;Mattia Alex Leoni ,&nbsp;Sara Remogna","doi":"10.1016/j.cam.2026.117376","DOIUrl":"10.1016/j.cam.2026.117376","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"483 ","pages":"Article 117376"},"PeriodicalIF":2.6,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146079948","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Efficient stability-preserving schemes for stochastic McKean-Vlasov equations with uncertainty","authors":"Haiyan Yuan ,&nbsp;Quanxin Zhu","doi":"10.1016/j.cam.2026.117361","DOIUrl":"10.1016/j.cam.2026.117361","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"483 ","pages":"Article 117361"},"PeriodicalIF":2.6,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146039555","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Double inertial contraction method for monotone inclusion problems for medical image recovery and data classifications","authors":"Pongsakorn Sunthrayuth ,&nbsp;Prasit Cholamjiak ,&nbsp;Issara Siramaneerat ,&nbsp;Jen-Chih Yao","doi":"10.1016/j.cam.2026.117369","DOIUrl":"10.1016/j.cam.2026.117369","url":null,"abstract":"<div><div>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 <em>R</em>-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.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"483 ","pages":"Article 117369"},"PeriodicalIF":2.6,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146039578","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An efficient matrix free optimization algorithm combining a revised PRP and FR-CG type methods with application to robotics","authors":"Nasiru Salihu ,&nbsp;Poom Kumam ,&nbsp;Aliyu Muhammed Awwal ,&nbsp;Mathew Remilekun Odekunle ,&nbsp;Thidaporn Seangwattana","doi":"10.1016/j.cam.2026.117378","DOIUrl":"10.1016/j.cam.2026.117378","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"483 ","pages":"Article 117378"},"PeriodicalIF":2.6,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146079949","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Novel Birkhoff-hermite ERKN methods for solving general second-order highly oscillatory systems","authors":"Yonglei Fang ,&nbsp;Changying Liu ,&nbsp;Xiong You","doi":"10.1016/j.cam.2026.117375","DOIUrl":"10.1016/j.cam.2026.117375","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"483 ","pages":"Article 117375"},"PeriodicalIF":2.6,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146079950","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Fröbenius expansions for second-order random differential equations: Stochastic analysis and applications to Lindley-type damping models","authors":"Halim Zeghdoudi ,&nbsp;Mohamed Amine Kerker ,&nbsp;Elif Boduroglu","doi":"10.1016/j.cam.2026.117379","DOIUrl":"10.1016/j.cam.2026.117379","url":null,"abstract":"<div><div>This paper develops a Frobenius series framework for the stochastic analysis of second–order random differential equations of the form<span><span><span><math><mrow><mover><mi>Y</mi><mo>¨</mo></mover><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>+</mo><mi>A</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mover><mi>Y</mi><mo>˙</mo></mover><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><mn>0</mn><mo>,</mo></mrow></math></span></span></span>where the damping coefficient <em>A</em>(<em>t</em>) is a positive stochastic process and the initial conditions are square–integrable random variables. Assuming mean–square analyticity of <em>A</em>(<em>t</em>) 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 <em>Y</em>(<em>t</em>) via Monte Carlo simulation. To improve computational efficiency, a control variates strategy is incorporated for variance reduction.</div><div>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.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"483 ","pages":"Article 117379"},"PeriodicalIF":2.6,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146079947","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Optimizing liquidity provision in Uniswap v3 via physics-informed neural networks","authors":"Salvatore Cuomo ,&nbsp;Federico Gatta ,&nbsp;Vincenzo Vocca","doi":"10.1016/j.cam.2026.117368","DOIUrl":"10.1016/j.cam.2026.117368","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"483 ","pages":"Article 117368"},"PeriodicalIF":2.6,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146039580","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}