Mathematics and Computers in Simulation最新文献

{"title":"Chebyshev delta shaped and Chebyshev pseudo-spectral methods for solutions of differential equations","authors":"Fahir Talay Akyildiz ,&nbsp;Kuppalapalle Vajravelu ,&nbsp;Cemil Tunç ,&nbsp;John Abraham","doi":"10.1016/j.matcom.2025.03.034","DOIUrl":"10.1016/j.matcom.2025.03.034","url":null,"abstract":"<div><div>In this paper we introduce a new Chebyshev delta-shaped function (CDSF) and establish its relationship with Chebyshev polynomials in interpolation problems. We first prove that CDSF is indeed form a basis for a Haar space. We then derive the conditions for the selection of suitable collocation points. Next, we introduce and develop Chebyshev delta-shaped pseudo-spectral method. Error bounds on discrete <span><math><mrow><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>−</mo></mrow></math></span>norm and Sobolev norm <span><math><mrow><mfenced><mrow><msup><mrow><mi>H</mi></mrow><mrow><mi>p</mi></mrow></msup></mrow></mfenced></mrow></math></span> are presented for the Chebyshev pseudo-spectral method. Tests to find approximate solutions for the Poisson, Poisson-Boltzmann equations and Stokes second problem and comparisons of the predictions using the following methods are presented:</div><div><ul><li><span>1.</span><span><div>Chebyshev pseudo-spectral method,</div></span></li><li><span>2.</span><span><div>Cosine-sine delta-shaped pseudo-spectral method, and</div></span></li><li><span>3.</span><span><div>Cosine-sine pseudo-spectral method.</div></span></li></ul></div><div>Excellent convergent and stable results are obtained by using our newly defined Chebyshev delta-shaped basis functions and this is documented for the first time.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"236 ","pages":"Pages 52-69"},"PeriodicalIF":4.4,"publicationDate":"2025-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143817439","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":"H2 optimal model reduction of linear dynamical systems with quadratic output by the Riemannian BFGS method","authors":"Ping Yang ,&nbsp;Zhao-Hong Wang ,&nbsp;Yao-Lin Jiang","doi":"10.1016/j.matcom.2025.03.021","DOIUrl":"10.1016/j.matcom.2025.03.021","url":null,"abstract":"<div><div>This paper considers the <span><math><msub><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> optimal model reduction problem of linear dynamical systems with quadratic output on the Riemannian manifolds. A one-sided projection is used to reduce the state equation, while a suitable symmetric matrix is chosen to determine the output equation of the reduced system. Since the projection matrix is an orthonormal matrix, it can be seen as a point on the Stiefel manifold. Because symmetric matrices of the same dimension allow a manifold structure, it is used to define a product manifold combined with the Stiefel manifold. The <span><math><msub><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> error between the original system and the reduced system is treated as a function defined on the product manifold. Then, the <span><math><msub><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> optimal model reduction problem is formulated as an unconstrained optimization problem defined on the product manifold. Concerning the symmetric matrix, the <span><math><msub><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> error is proved to be convex. In terms of the orthonormal matrix and the symmetric matrix, the gradients of the <span><math><msub><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> error are derived respectively. Then, the Riemannian BFGS method is used to obtain the orthonormal matrix, and the symmetric matrix is calculated by the convexity and the related gradient. By introducing the Riemannian manifolds to the <span><math><msub><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> optimal model reduction problem, the constrained optimization problem in the Euclidean space is transformed into an unconstrained optimization problem on the manifolds, and the gradients of the <span><math><msub><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> error are equipped with relatively concise formulas. Finally, numerical results illustrate the performance of the proposed model reduction method.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"236 ","pages":"Pages 1-11"},"PeriodicalIF":4.4,"publicationDate":"2025-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143792033","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":"Data-driven fractional algebraic system solver","authors":"Emmanuel Lorin ,&nbsp;Howl Nhan","doi":"10.1016/j.matcom.2025.03.004","DOIUrl":"10.1016/j.matcom.2025.03.004","url":null,"abstract":"<div><div>In this paper, we explore a class of (data-driven<span><math><mo>/</mo></math></span>supervised) neural network-based algorithms for solving linear and fractional algebraic systems. The latter are reformulated as dynamical systems, and solved using neural networks. Some mathematical proprieties of the derived algorithms are proposed, as well as several illustrating numerical experiments.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"236 ","pages":"Pages 170-182"},"PeriodicalIF":4.4,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143833434","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 and long time stable IMEX schemes for the unsteady dual-porosity-Stokes system","authors":"Yi Li ,&nbsp;Ning Li ,&nbsp;Dandan Xue ,&nbsp;Yi Qin","doi":"10.1016/j.matcom.2025.03.026","DOIUrl":"10.1016/j.matcom.2025.03.026","url":null,"abstract":"<div><div>In this paper, we introduce an efficient and long time stable implicit–explicit(IMEX) scheme for the dual-porosity-Stokes equations. On the basis of backward Euler scheme and the solution at previous time level, we apply implicit discretization for sub-problems terms and explicit discretization for interface terms. By introducing a new scalar auxiliary variable (SAV), the scheme avoids time step constraints in long time stability analysis. We derive the error estimates of the full discretization with finite element method for the spatial discretization without any time step conditions. Moreover, we extend the approach to higher order IMEX schemes and develop variable time stepsize adaptive algorithm using time filter. Numerical tests are provided to validate the accuracy of several numerical schemes and assess industrial applicability of the coupled model in the multistage fractured horizontal wellbore problem.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"236 ","pages":"Pages 111-134"},"PeriodicalIF":4.4,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143833505","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":"Shape-preserving subdivision scheme with the third-order accuracy and C2 smoothness","authors":"Yejin Kim ,&nbsp;Hyoseon Yang ,&nbsp;Jungho Yoon","doi":"10.1016/j.matcom.2025.03.030","DOIUrl":"10.1016/j.matcom.2025.03.030","url":null,"abstract":"<div><div>In this study, we present a novel shape preserving <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> subdivision scheme with third-order accuracy. Its limit functions preserve both monotonicity and convexity of the given data, even in cases where the data are non-strictly monotone or convex. To achieve this, we especially devise a modified <em>minmod</em> method, originally introduced in Gelb and Tadmor (2006) to detect edges from a piecewise smooth data, that plays a role of limiting procedure to prevent spurious oscillations. While most of shape preserving schemes are complicated, the proposed method is conceptually simple to implement. Some numerical results are presented to demonstrate the accuracy, smoothness and shape preserving performance of the proposed scheme.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"235 ","pages":"Pages 160-174"},"PeriodicalIF":4.4,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143785543","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":"A lattice-based approach for life insurance pricing in a stochastic correlation framework","authors":"Massimo Costabile ,&nbsp;Ivar Massabó ,&nbsp;Emilio Russo ,&nbsp;Alessandro Staino ,&nbsp;Rogemar Mamon ,&nbsp;Yixing Zhao","doi":"10.1016/j.matcom.2025.03.027","DOIUrl":"10.1016/j.matcom.2025.03.027","url":null,"abstract":"<div><div>We propose a new implementation approach in insurance product valuation to capture the stochastic correlation between financial and demographic factors. This is important to accommodate the prevailing situation where the interest rate and mortality intensity move jointly and randomly. A stochastic correlation model is considered where it follows a diffusion process that may assume the form of a bounded Jacobi process or of a transformed modified Ornstein–Uhlenbeck process. Our contributions strengthen the general modelling set up of dependent financial and actuarial risks. We put forward a discrete-time pricing model that supports the valuation of a relatively wide class of insurance products. Specifically, the pricing of contracts, with an embedded surrender option for which no explicit formulae are available, is facilitated with ease. We customise the construction of lattice discretisations that admit a large set of risk processes having appropriate specifications. In particular, the interest rate, mortality and correlation dynamics are discretised via three different binomial lattices that are then assembled to create a trivariate lattice structured with eight branches for each node. Numerical experiments involving some stylised insurance contracts are conducted. Such experiments confirm the accuracy and efficiency of our proposed approach with respect to two benchmarks: the Monte-Carlo simulation method, and the method and results by Devolder et al. (2024).</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"235 ","pages":"Pages 145-159"},"PeriodicalIF":4.4,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143777370","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Design of secure S-Boxes via novel 2D-Zettle chaotic map and ABC algorithm for robust image encryption","authors":"Deniz Ustun ,&nbsp;Serap Sahinkaya","doi":"10.1016/j.matcom.2025.03.019","DOIUrl":"10.1016/j.matcom.2025.03.019","url":null,"abstract":"<div><div>This work addresses the challenge of improving security in chaos-based cryptographic systems by introducing a more effective chaotic map that is derived from the Zettle test function, providing better resistance to attacks and ensuring higher security. The design of secure S-Boxes for the R, G, and B colour channels is a critical challenge in colour image encryption. The proposed method addresses this challenge by significantly enhancing security through the use of the ABC algorithm in conjunction with the novel 2D-Zettle chaotic map. Additionally, the proposed image encryption technique addresses the problem of optimizing key selection for both encryption and decryption, ensuring robust security against various attacks and noise, as demonstrated by extensive performance evaluations. Furthermore, security assessments, including statistical analyses and resilience tests against various attacks and noise, confirm the method’s exceptional efficiency and broad applicability in safeguarding digital assets.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"235 ","pages":"Pages 175-204"},"PeriodicalIF":4.4,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143785544","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":"On the stability of the PPH subdivision scheme on nonuniform grids","authors":"Pedro J. Martínez-Aparicio ,&nbsp;Pedro Ortiz ,&nbsp;Juan Carlos Trillo","doi":"10.1016/j.matcom.2025.03.028","DOIUrl":"10.1016/j.matcom.2025.03.028","url":null,"abstract":"<div><div>Our purpose in this article is to prove the stability of the subdivision scheme associated with the PPH reconstruction on nonuniform grids. This subdivision scheme is convexity preserving and therefore quite interesting from the practical point of view. Therefore, it is also of utmost importance to count with a stability result ensuring its applicability in real cases. The theoretical stability has been proven for <span><math><mrow><mn>3</mn><mo>−</mo><mi>l</mi><mi>o</mi><mi>c</mi><mi>a</mi><mi>l</mi></mrow></math></span> <span><math><mi>σ</mi></math></span> quasi-uniform grids with <span><math><mrow><mi>σ</mi><mo>≤</mo><mn>3</mn><msqrt><mrow><mn>5</mn></mrow></msqrt><mo>−</mo><mn>5</mn><mo>.</mo></mrow></math></span> In the numerical experiments we analyze the sharpness of the given stability bound and of the restriction on the grids.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"236 ","pages":"Pages 154-169"},"PeriodicalIF":4.4,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143833433","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":"Modelling of the additional motion resistance term in CFD simulations using porosity distributed resistance (PDR)","authors":"Estevão G.C. Barreto ,&nbsp;Tânia S. Klein ,&nbsp;Sávio S.V. Vianna","doi":"10.1016/j.matcom.2025.03.024","DOIUrl":"10.1016/j.matcom.2025.03.024","url":null,"abstract":"<div><div>The numerical simulation of turbulent flows through groups of obstacles is essential in various industrial applications, particularly in the numerical modelling of accidental explosions. In such contexts, particular attention must be given to small-scale objects that impose flow resistance and contribute to turbulence generation. The Porosity Distributed Resistance (PDR) approach has been introduced as a practical method to address the complexity of simulating flow behaviour near small-scale objects. This study presents a novel model for the additional motion resistance term (<span><math><msub><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span>) within Computational Fluid Dynamics (CFD) simulations, specifically designed to enhance the PDR approach. Using CFD simulations conducted in CFX, we derived and validated the <span><math><msub><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> model by comparing simulation results with empirical correlations, demonstrating its dependence on cell volumetric porosity. This model was subsequently implemented and tested in STOKES, a CFD software tailored for explosion simulations that incorporates the PDR methodology. Our study also investigated the effects of computational mesh resolution on porosity distribution within the domain. Two key conclusions emerged: first, the proposed model significantly improves simulation accuracy when coarse computational meshes are employed—typical for large-scale industrial simulations, including gas dispersion and explosion scenarios; second, at finer mesh resolutions, the PDR concept renders the <span><math><msub><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> model impact negligible. Consequently, an influence radius is recommended for activating the <span><math><msub><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> term, ensuring optimal application within the computational domain.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"235 ","pages":"Pages 132-144"},"PeriodicalIF":4.4,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143777371","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":"Dynamics of solitons and modulation instability in a (2+1)-dimensional coupled nonlinear Schrödinger equation","authors":"Vineesh Kumar ,&nbsp;Arvind Patel ,&nbsp;Monu Kumar","doi":"10.1016/j.matcom.2025.03.022","DOIUrl":"10.1016/j.matcom.2025.03.022","url":null,"abstract":"<div><div>This study uses the complex amplitude ansatz and semi-inverse methods to explore the closed-form exact optical soliton solutions of a (2+1)-dimensional coupled nonlinear Schrödinger (NLS) equation. Delving into the specified methods unveils the enigmatic dynamic presence of solitons within the solutions of the NLS equation. These methods produce specific possible solutions of the equation that contain enough free physical parameters. Also, the phase shift and intensity of the soliton solutions are presented. The results of produced solutions are reported as bright, anti-bright, dark, kink, anti-kink, stationary, and one-solitons. This study explores soliton solution of the NLS equation not known earlier. Furthermore, we performed a comprehensive modulation instability (MI) analysis using linear standard stability analysis, providing valuable insights into this phenomenon. Graphical representations of the solutions such as two-dimensional (2D), three-dimensional (3D), and contour plots have been illustrated with appropriate parameter values to provide additional insight into these innovative solutions. It is found that MI gain and instability bandwidth can be controlled by the equations parameter, initial incidence power and perturbation wave numbers.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"235 ","pages":"Pages 95-113"},"PeriodicalIF":4.4,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143761330","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}