Mathematics and Computers in Simulation最新文献

{"title":"Vertical modeling of carbon sequestration in coastal wetlands using fractional-order derivatives and moisture dynamics","authors":"Vsevolod Bohaienko ,&nbsp;Fasma Diele ,&nbsp;Fabio V. Difonzo ,&nbsp;Carmela Marangi ,&nbsp;Angela Martiradonna ,&nbsp;Antonello Provenzale","doi":"10.1016/j.matcom.2025.02.005","DOIUrl":"10.1016/j.matcom.2025.02.005","url":null,"abstract":"<div><div>Wetlands are essential for global biogeochemical cycles and ecosystem services, with the dynamics of soil organic carbon (SOC) serving as the critical regulatory mechanism for these processes. However, accurately modeling carbon dynamics in wetlands presents challenges due to their complexity. Traditional approaches often fail to capture spatial variations, long-range transport, and periodical flooding dynamics, leading to uncertainties in carbon flux predictions. To tackle these challenges, we introduce a novel extension of the fractional RothC model, integrating temporal fractional-order derivatives into spatial dimensions. This enhancement allows for the creation of a more adaptive tool for analyzing SOC dynamics. Our differential model incorporates Richardson–Richard’s equation for moisture fluxes, a diffusion–advection–reaction equation for fractional-order dynamics of SOC compounds, and a temperature transport equation. We examine the influence of diffusive movement and sediment moisture content on model solutions, as well as the impact of including advection terms. Finally, we validated the model on a restored wetland scenario at the Ebro Delta site, aiming to evaluate the effectiveness of flooding strategies in enhancing carbon sequestration and ecosystem resilience.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"233 ","pages":"Pages 369-388"},"PeriodicalIF":4.4,"publicationDate":"2025-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143427935","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":"Multi-period mean–variance portfolio optimization with capital injections","authors":"Longyu Shi ,&nbsp;Yunyun Wang ,&nbsp;Wenyue Li ,&nbsp;Zhimin Zhang","doi":"10.1016/j.matcom.2025.02.006","DOIUrl":"10.1016/j.matcom.2025.02.006","url":null,"abstract":"<div><div>In this study, we explore the portfolio optimization problem where the investors initially allocate portions of their capital across a large asset pool, followed by gradual capital injections over the subsequent periods. We introduce a multi-period mean–variance model with capital injections to develop a sparse long-term investment strategy within this framework. This model adopts the fused Lasso technique, integrating two <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> penalty terms designed to lower both holding and trading costs. We utilize a two-block alternating direction method of multipliers algorithm to solve this complex, non-smooth optimization problem involving multiple variables. A thorough analysis of the convergence of the algorithm is provided. In addition, we empirically validate the efficacy of our model using two real datasets, demonstrating its practical applicability and effectiveness in real-world scenarios.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"233 ","pages":"Pages 400-412"},"PeriodicalIF":4.4,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143437020","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":"Effect of space discretization on the parareal algorithm for advection-diffusion equations","authors":"Xianfu Zeng ,&nbsp;Haiyan Song","doi":"10.1016/j.matcom.2025.02.007","DOIUrl":"10.1016/j.matcom.2025.02.007","url":null,"abstract":"<div><div>The influence of time-integrator on the convergence rate of the parallel-in-time algorithm parareal has been extensively studied in literature, but the effect of space discretization was only rarely considered. In this paper, using the advection–diffusion equation parametrized by a diffusion coefficient <span><math><mrow><mi>ν</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span> as the model, we show that the space discretization indeed has a non-negligible effect on the convergence rate, especially when <span><math><mi>ν</mi></math></span> is small. In particular, for two space discretizations—the centered FD (finite difference) method and a Compact FD method of order 4, we show that the algorithm converges with very different rates, even though both the coarse and fine solvers of the algorithm are strongly stable under these two space discretizations. Numerical results for one-dimensional and two-dimensional cases are presented to validate the theoretical predictions.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"233 ","pages":"Pages 330-340"},"PeriodicalIF":4.4,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143420997","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":"Modeling the effects of obesity on a tumor-immune model with combined therapy","authors":"Wenjie Qin ,&nbsp;Yi Zhao ,&nbsp;Jin Yang","doi":"10.1016/j.matcom.2025.02.004","DOIUrl":"10.1016/j.matcom.2025.02.004","url":null,"abstract":"<div><div>This paper examines and analyzes a mathematical model that describes the interactions between tumors, immune cells, healthy cells, and stored fat in the body. The model incorporates integrated therapy as a key component of the analysis. We first prove that the system exists with a global positive solution which is unique. Subsequently, we derive threshold conditions determining the elimination and persistence of tumor cells, immune cells and fat cells, employing Stochastic Differential Equations theory. Additionally, we investigate the system’s smooth distribution and its ergodic properties. The results indicate that therapies marked by pronounced stochastic disturbances, elevated medication dosages or shortened treatment cycles can effectively hinder tumor growth and simultaneously promote weight loss. A low-calorie diet leads to a decrease in body weight and a reduction in tumor cells, underscoring the potential benefits of weight management as a supplementary strategy to chemotherapy. Notably, combination therapy reduces the detrimental effects of chemotherapy on healthy cells.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"233 ","pages":"Pages 276-295"},"PeriodicalIF":4.4,"publicationDate":"2025-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143395207","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 L2 approximation by planar Pythagorean-hodograph curves","authors":"Rida T. Farouki ,&nbsp;Marjeta Knez ,&nbsp;Vito Vitrih ,&nbsp;Emil Žagar","doi":"10.1016/j.matcom.2025.02.001","DOIUrl":"10.1016/j.matcom.2025.02.001","url":null,"abstract":"<div><div>The <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> approximation of planar curves by Pythagorean-hodograph (PH) polynomial curves is addressed, based on the distance defined by a metric for planar curves represented as complex-valued functions of a real parameter. Because of the nonlinear nature of polynomial PH curves, constructing <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> approximants involves solving a nonlinear optimization problem. However, a simplified method that requires only the solution of a linear system may be developed by formulating the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> approximation in the preimage space. The extension of the methodology to approximation by PH B-spline curves is also addressed, and several examples are provided to illustrate its implementation and potential.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"233 ","pages":"Pages 296-310"},"PeriodicalIF":4.4,"publicationDate":"2025-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143395208","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":"Improved fuzzy C-means clustering algorithm based on fuzzy particle swarm optimization for solving data clustering problems","authors":"Hongkang Zhang,&nbsp;Shao-Lun Huang","doi":"10.1016/j.matcom.2025.02.012","DOIUrl":"10.1016/j.matcom.2025.02.012","url":null,"abstract":"<div><div>The fuzzy c-means (FCM) clustering algorithm is adversely affected by its sensitivity to initial values and its low clustering accuracy. To mitigate these shortcomings, we proposed an improved fuzzy particle swarm optimization-fuzzy C-Means (IFPSO-FCM) algorithm to resolve the data-clustering challenges. In this algorithm, key enhancements included initializing clustering centers using Mahalanobis distances to alleviate the sensitivity to initial values. An objective function based on both inter- and intra-cluster evaluations was proposed to address the premature convergence. A modified particle swarm algorithm was designed to optimize the clustering centers. The proposed algorithm was applied to analyze the IRIS and WINE datasets, as well as to cluster and segment classical test images. The results indicated that the algorithm improved the stability of the analysis results while preserving high clustering accuracy and convergence speed, achieving an excellent performance compared with existing methods. Moreover, it exhibited superior performance in the analysis of fuzzy multi-shadow gray images.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"233 ","pages":"Pages 311-329"},"PeriodicalIF":4.4,"publicationDate":"2025-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143421000","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 investigation into the impact of odour: A dynamical study of two predators and one prey model, taking into account both integer order and fractional order derivatives","authors":"Dipam Das ,&nbsp;Debasish Bhattacharjee","doi":"10.1016/j.matcom.2025.01.026","DOIUrl":"10.1016/j.matcom.2025.01.026","url":null,"abstract":"<div><div>This article presents a prey–predator system that takes into account two important factors: the negative impact of predator odour on its competitors and the positive impact of predator odour on the prey. The system is analysed using two models: one with ODEs and another with FDEs. We have extensively validated the model system biologically, ensuring that the solutions are both nonnegative and bounded. An in-depth investigation has been carried out to thoroughly investigate the stability of all potential equilibrium points of the model systems in a systematic manner. Our observations reveal that our model systems exhibit various types of bifurcations, including transcritical and Hopf bifurcations, around the interior equilibrium point for three distinct parameters. These parameters include the rate of conversion of the first predator <span><math><msub><mrow><mi>r</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span>, the degree of resistance or avoidance exhibited by the prey due to predator odour <span><math><mi>m</mi></math></span>, and the level of disruption to competitors in predation due to the presence of predator odour <span><math><mi>a</mi></math></span>. A significant finding in this paper is that the resistance shown by prey towards the first predator in predation in reaction to the odour is vital for sustaining the population of the second predator. The survival of the second predator within the biosystem is heavily dependent on the growth rate of the first predator. The possibility of the second predator facing extinction becomes much less likely when the first predator is absent from the system, which is another significant result. Within the context of fractional order derivatives, the system dynamics demonstrate a higher level of stability in comparison to the traditional integer order derivative. It has been noticed that where the parameter values are identical, the fluctuations exhibited by the integer order system are stabilised in the fractional order system. Thus, the significance of predator odour and the effect of memory in the system have been thoroughly established. Ultimately, the study backs up the theoretical findings with convincing numerical simulations.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"233 ","pages":"Pages 341-368"},"PeriodicalIF":4.4,"publicationDate":"2025-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143421001","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":"Uniform error bounds of an exponential wave integrator for the Klein–Gordon–Schrödinger system in the nonrelativistic and massless limit regime","authors":"Jiyong Li,&nbsp;Minghui Yang","doi":"10.1016/j.matcom.2025.01.027","DOIUrl":"10.1016/j.matcom.2025.01.027","url":null,"abstract":"&lt;div&gt;&lt;div&gt;We propose an exponential wave integrator Fourier pseudo-spectral (EWI-FP) method and establish the uniform error bounds for the Klein–Gordon–Schrödinger system (KGSS) with &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;ɛ&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;. In the nonrelativistic and massless limit regime (&lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mi&gt;ɛ&lt;/mi&gt;&lt;mo&gt;≪&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;), the solution of KGSS propagates waves with wavelength &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;O&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;ɛ&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; in time and amplitude at &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;O&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;ɛ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;†&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; where &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;†&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;min&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; with two parameters &lt;span&gt;&lt;math&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;. The parameters satisfy &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;. In this regime, due to the oscillation in time, it is very difficult to develop efficient schemes and make the corresponding error analysis for KGSS. In this paper, firstly, in order to overcome the difficulty of controlling the nonlinear terms, we transform the KGSS into a system with higher derivative. Then we construct an EWI-FP method and provide the error estimates with two bounds at &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;O&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mo&gt;min&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mi&gt;τ&lt;/mi&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;ɛ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;∗&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;τ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;ɛ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;†&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;O&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;τ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;ɛ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;†&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, respectively, where &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;∗&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;min&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; has to do with the smoothness of the solution in space, &lt;span&gt;&lt;math&gt;&lt;mi&gt;h&lt;/mi&gt;","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"233 ","pages":"Pages 237-258"},"PeriodicalIF":4.4,"publicationDate":"2025-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143378417","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":"Numerical integration of Navier–Stokes equations by time series expansion and stabilized FEM","authors":"Ahmad Deeb ,&nbsp;Denys Dutykh","doi":"10.1016/j.matcom.2025.01.023","DOIUrl":"10.1016/j.matcom.2025.01.023","url":null,"abstract":"<div><div>This manuscript introduces an advanced numerical approach for the integration of incompressible Navier-Stokes (NS) equations using a Time Series Expansion (TSE) method within a Finite Element Method (FEM) framework. The technique is enhanced by a novel stabilization strategy, incorporating a Divergent Series Resummation (DSR) technique, which significantly augments the computational efficiency of the algorithm. The stabilization mechanism is meticulously designed to improve the stability and validity of computed series terms, enabling the application of the Factorial Series (FS) algorithm for series resummation. This approach is pivotal in addressing the challenges associated with the accurate and stable numerical solution of NS equations, which are critical in Computational Fluid Dynamics (CFD) applications. The manuscript elaborates on the variational formulation of Stokes problem and present convergence analysis of the method using the Ladyzhenskaya–Babuvska–Brezzi (LBB) condition. It is followed by the NS equations and the implementation details of the stabilization technique, underscored by numerical tests on laminar flow past a cylinder, showcasing the method’s efficacy and potential for broad applicability in fluid dynamics simulations. The results of the stabilization indicate a substantial enhancement in computational stability and accuracy, offering a promising avenue for future research in the field.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"233 ","pages":"Pages 208-236"},"PeriodicalIF":4.4,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143349231","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":"Symmetry methods and multi-structure solutions for a (3+1)-dimensional generalized nonlinear evolution equation","authors":"Uttam Kumar Mandal ,&nbsp;Biren Karmakar ,&nbsp;Sukanya Dutta ,&nbsp;Amiya Das","doi":"10.1016/j.matcom.2025.01.018","DOIUrl":"10.1016/j.matcom.2025.01.018","url":null,"abstract":"<div><div>In this paper, we investigate a novel <span><math><mrow><mo>(</mo><mn>3</mn><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math></span>-dimensional generalized Painlevè-integrable nonlinear evolution equation. Employing a dependent variable transformation, we derive the Hirota bilinear form, leading to the discovery of one, two, and three kink-soliton solutions for the equation. Furthermore, by substituting a quadratic-type test function into the Hirota bilinear form, we obtain lump solutions. Additionally, we extend our findings to include lump-multi-kink solutions using two distinct types of test functions. Furthermore, we establish two separate bilinear Bäcklund transformations using two different exchange identities, each characterized by its own set of arbitrary parameters. The first Bäcklund transformation form includes seven arbitrary parameters, while the second form features four arbitrary parameters. Our work also results in the discovery of a new exact traveling wave solution under various parametric conditions for our model. We delve into the dynamical behavior of these solutions, particularly in the long wave limit. Moreover, we explore the Lie point symmetries of our model equation, leading to the identification of new exact solutions arising from symmetry reduction.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"233 ","pages":"Pages 259-275"},"PeriodicalIF":4.4,"publicationDate":"2025-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143378418","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}