Pub Date : 2024-11-10DOI: 10.1016/j.matcom.2024.11.003
Wen-Ze Wu , Jie Xu , Wanli Xie , Tao Zhang
In order to expand the applicability of the conventional fractional grey model, an innovative fractional grey model is proposed by the introduction of the innovative fractional accumulation. Three efforts are made in this study. First, the innovative fractional accumulation and its inverse operation are designed. Based on the innovative form, the parameter estimation and discrete time response of the novel model are given. In addition, the moth flame optimization algorithm is used to determine optimal hyper parameters for the novel model, and the rolling mechanism is used to enhance the prediction performance. To comprehensively confirm the forecasting ability of the proposed model, it is applied in three kinds of data with inverted U-shaped, W-shaped and oscillating features. The experimental results show the novel model is superior to all competitors in terms of level accuracy. Therefore, the novel model is considered a promising method for enhancing the existing fractional grey model.
为了扩大传统分数灰色模型的适用性，本研究通过引入创新的分数累积法，提出了一种创新的分数灰色模型。本研究做了三方面的工作。首先，设计了创新型分数累加及其逆运算。在创新形式的基础上，给出了新模型的参数估计和离散时间响应。此外，利用蛾焰优化算法确定了新型模型的最优超参数，并利用滚动机制提高了预测性能。为了全面证实所提模型的预测能力，将其应用于具有倒 U 形、W 形和振荡特征的三种数据中。实验结果表明，就水平精度而言，新模型优于所有竞争对手。因此，新模型被认为是增强现有分数灰色模型的一种有前途的方法。
{"title":"An innovative fractional grey system model and its application","authors":"Wen-Ze Wu , Jie Xu , Wanli Xie , Tao Zhang","doi":"10.1016/j.matcom.2024.11.003","DOIUrl":"10.1016/j.matcom.2024.11.003","url":null,"abstract":"<div><div>In order to expand the applicability of the conventional fractional grey model, an innovative fractional grey model is proposed by the introduction of the innovative fractional accumulation. Three efforts are made in this study. First, the innovative fractional accumulation and its inverse operation are designed. Based on the innovative form, the parameter estimation and discrete time response of the novel model are given. In addition, the moth flame optimization algorithm is used to determine optimal hyper parameters for the novel model, and the rolling mechanism is used to enhance the prediction performance. To comprehensively confirm the forecasting ability of the proposed model, it is applied in three kinds of data with inverted U-shaped, W-shaped and oscillating features. The experimental results show the novel model is superior to all competitors in terms of level accuracy. Therefore, the novel model is considered a promising method for enhancing the existing fractional grey model.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"230 ","pages":"Pages 68-79"},"PeriodicalIF":4.4,"publicationDate":"2024-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142659324","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}
Pub Date : 2024-11-09DOI: 10.1016/j.matcom.2024.11.001
Shweta , Gourav Arora , Rajesh Kumar
The behavior of several particulate processes, such as cell interaction, blood clotting, bubble formation, grain breakage, and cheese formation from milk, have been studied using coagulation and fragmentation models (Fogelson and Guy, 2008 [1]; Pazmiño et al., 2022 [2]; Chen et al., [3]). Various studies utilize the linear fragmentation model to simplify the underlying physics. However, in real-life scenarios, particles form due to the collision of two particles, leading to a non-linear collisional breakage model. Unfortunately, the collisional breakage model is less explored due to its complex behavior. While analytical solutions are difficult to compute and are still missing in the literature, this article proposes an approximate solution for the model using the Laplace-based accelerated homotopy perturbation method. Further, coupling with Padé approximant, the accuracy of the solution is extended for the longer time. Considering various physically relevant kernels, the approximate series solutions are compared with the well known finite-volume solutions to measure the accuracy in terms of qualitative and quantitative errors. The article also encompasses theoretical convergence analysis and error estimations to enhance comprehension of the proposed formulation.
{"title":"Large time solution for collisional breakage model: Laplace transformation based accelerated homotopy perturbation method","authors":"Shweta , Gourav Arora , Rajesh Kumar","doi":"10.1016/j.matcom.2024.11.001","DOIUrl":"10.1016/j.matcom.2024.11.001","url":null,"abstract":"<div><div>The behavior of several particulate processes, such as cell interaction, blood clotting, bubble formation, grain breakage, and cheese formation from milk, have been studied using coagulation and fragmentation models (Fogelson and Guy, 2008 <span><span>[1]</span></span>; Pazmiño et al., 2022 <span><span>[2]</span></span>; Chen et al., <span><span>[3]</span></span>). Various studies utilize the linear fragmentation model to simplify the underlying physics. However, in real-life scenarios, particles form due to the collision of two particles, leading to a non-linear collisional breakage model. Unfortunately, the collisional breakage model is less explored due to its complex behavior. While analytical solutions are difficult to compute and are still missing in the literature, this article proposes an approximate solution for the model using the Laplace-based accelerated homotopy perturbation method. Further, coupling with Padé approximant, the accuracy of the solution is extended for the longer time. Considering various physically relevant kernels, the approximate series solutions are compared with the well known finite-volume solutions to measure the accuracy in terms of qualitative and quantitative errors. The article also encompasses theoretical convergence analysis and error estimations to enhance comprehension of the proposed formulation.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"230 ","pages":"Pages 39-52"},"PeriodicalIF":4.4,"publicationDate":"2024-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142659322","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}
Pub Date : 2024-11-09DOI: 10.1016/j.matcom.2024.11.002
Ibrahim O. Sarumi , Khaled M. Furati , Abdul Q.M. Khaliq
Time-fractional advection–diffusion–reaction type equations are useful for characterizing anomalous transport processes. In this paper, linearly implicit as well as explicit generalized exponential time differencing (GETD) schemes are proposed for solving a class of such equations having time–space dependent coefficients. The implicit scheme, being unconditionally stable, is robust in handling the numerical instabilities in problems where the advection term is dominant. Regarding the error analysis, uniformly optimal second-order convergence rates are derived using time-graded meshes to counter the effect of the inherent singularity of the continuous solution. Implementation of generalized exponential integrators requires computing the action of Mittag-Leffler function of matrices on a vector, or on a matrix in the case of the implicit scheme. For cost-effective implementation, using global Padé approximants these computation tasks get reduced to solving linear systems. A new approach based on Sylvester equation formulation of the resulting linear systems is developed in this paper. This technique leads to significantly faster algorithms for implementing the GETD schemes. Numerical experiments are provided to illustrate the theoretical findings and to assert the efficiency of the Sylvester equation based approach. Application of this approach to an existing GETD scheme for solving a nonlinear subdiffusion problem is also discussed.
{"title":"Efficient second-order accurate exponential time differencing for time-fractional advection–diffusion–reaction equations with variable coefficients","authors":"Ibrahim O. Sarumi , Khaled M. Furati , Abdul Q.M. Khaliq","doi":"10.1016/j.matcom.2024.11.002","DOIUrl":"10.1016/j.matcom.2024.11.002","url":null,"abstract":"<div><div>Time-fractional advection–diffusion–reaction type equations are useful for characterizing anomalous transport processes. In this paper, linearly implicit as well as explicit generalized exponential time differencing (GETD) schemes are proposed for solving a class of such equations having time–space dependent coefficients. The implicit scheme, being unconditionally stable, is robust in handling the numerical instabilities in problems where the advection term is dominant. Regarding the error analysis, uniformly optimal second-order convergence rates are derived using time-graded meshes to counter the effect of the inherent singularity of the continuous solution. Implementation of generalized exponential integrators requires computing the action of Mittag-Leffler function of matrices on a vector, or on a matrix in the case of the implicit scheme. For cost-effective implementation, using global Padé approximants these computation tasks get reduced to solving linear systems. A new approach based on Sylvester equation formulation of the resulting linear systems is developed in this paper. This technique leads to significantly faster algorithms for implementing the GETD schemes. Numerical experiments are provided to illustrate the theoretical findings and to assert the efficiency of the Sylvester equation based approach. Application of this approach to an existing GETD scheme for solving a nonlinear subdiffusion problem is also discussed.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"230 ","pages":"Pages 20-38"},"PeriodicalIF":4.4,"publicationDate":"2024-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142659492","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}
Pub Date : 2024-11-07DOI: 10.1016/j.matcom.2024.10.041
Daniele Peri
In this paper, a multidisciplinary design optimization algorithm, the Normal Boundary Intersection (NBI) method, is applied to the design of some devices of a sailing yacht. The full Pareto front is identified for two different design problems, and the optimal configurations are compared with standard devices. The great efficiency of the optimization algorithm is demonstrated by the wideness and density of the identified Pareto front.
{"title":"Multi-objective optimization of the appendages of a sailing yacht using the Normal Boundary Intersection method","authors":"Daniele Peri","doi":"10.1016/j.matcom.2024.10.041","DOIUrl":"10.1016/j.matcom.2024.10.041","url":null,"abstract":"<div><div>In this paper, a multidisciplinary design optimization algorithm, the Normal Boundary Intersection (NBI) method, is applied to the design of some devices of a sailing yacht. The full Pareto front is identified for two different design problems, and the optimal configurations are compared with standard devices. The great efficiency of the optimization algorithm is demonstrated by the wideness and density of the identified Pareto front.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"229 ","pages":"Pages 885-895"},"PeriodicalIF":4.4,"publicationDate":"2024-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142650624","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}
Pub Date : 2024-11-07DOI: 10.1016/j.matcom.2024.10.018
Bingzhen Chen , Wenjuan Zhai
In recent years, distributed statistical models have received increasing attention for large-scale data analysis. On the one hand, data sets come from multiple data sources, and are stored in different locations due to limited bandwidth and storage, or privacy protocols, directly centralizing all data together is impossible. On the other hand, the size of data is so large that it is difficult or inefficient to analyze data together. There are two main research aspects to using distributed statistical models to analyze large-scale data. The first one is to study the statistical convergence rate under some mild assumptions. The second one is to establish fast and efficient optimization algorithms considering the property of the loss function. There is a lot of research on the first aspect, but relatively little research on the second one. Motivated by this, we consider the construction of unified algorithms for distributed linear regression with different losses and regularizers. As a result, we designed two type methods, proximal alternating direction method of multipliers (pADMM) and distributed accelerated proximal gradient method with line-search (DAPGL). In order to demonstrate the efficiency of the proposed algorithms, we perform numerical experiments on the distributed Huber-Lasso model and Huber-Group-Lasso model. In view of the numerical results, we can observe that these two algorithms are more competitive than some of state-of-art algorithms. In particular, DAPGL algorithm performs better than pADMM in most cases.
{"title":"Unified algorithms for distributed regularized linear regression model","authors":"Bingzhen Chen , Wenjuan Zhai","doi":"10.1016/j.matcom.2024.10.018","DOIUrl":"10.1016/j.matcom.2024.10.018","url":null,"abstract":"<div><div>In recent years, distributed statistical models have received increasing attention for large-scale data analysis. On the one hand, data sets come from multiple data sources, and are stored in different locations due to limited bandwidth and storage, or privacy protocols, directly centralizing all data together is impossible. On the other hand, the size of data is so large that it is difficult or inefficient to analyze data together. There are two main research aspects to using distributed statistical models to analyze large-scale data. The first one is to study the statistical convergence rate under some mild assumptions. The second one is to establish fast and efficient optimization algorithms considering the property of the loss function. There is a lot of research on the first aspect, but relatively little research on the second one. Motivated by this, we consider the construction of unified algorithms for distributed linear regression with different losses and regularizers. As a result, we designed two type methods, proximal alternating direction method of multipliers (pADMM) and distributed accelerated proximal gradient method with line-search (DAPGL). In order to demonstrate the efficiency of the proposed algorithms, we perform numerical experiments on the distributed Huber-Lasso model and Huber-Group-Lasso model. In view of the numerical results, we can observe that these two algorithms are more competitive than some of state-of-art algorithms. In particular, DAPGL algorithm performs better than pADMM in most cases.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"229 ","pages":"Pages 867-884"},"PeriodicalIF":4.4,"publicationDate":"2024-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142659627","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}
Pub Date : 2024-11-07DOI: 10.1016/j.matcom.2024.10.042
Ruqi Li , Yurong Song , Min Li , Hongbo Qu , Guo-Ping Jiang
To analyze and predict the evolution of contagion dynamics, fractional derivative modeling has emerged as an important technique. However, inferring the dynamical structure of fractional-order models with high degrees of freedom poses a challenge. In this paper, to elucidate the spreading mechanism and non-local properties of disease evolution, we propose a novel fractional-order SEIHDR epidemiological model with variable parameters, incorporating fractional derivatives in the Caputo sense. We compute the basic reproduction number by the next-generation matrix and establish local and global stability conditions based on this reproduction number. By using the fractional Adams–Bashforth method, we validate dynamical behaviors at different equilibrium points in both autonomous and non-autonomous scenarios, while qualitatively analyze the effects of fractional order on the dynamics. To effectively address the inverse problem of the proposed fractional SEIHDR model, we construct a fractional Physics-Informed Neural Network framework to simultaneously infer time-dependent parameters, fractional orders, and state components. Graphical results based on the COVID-19 pandemic data from Canada demonstrate the effectiveness of the proposed framework.
{"title":"Dynamic analysis and data-driven inference of a fractional-order SEIHDR epidemic model with variable parameters","authors":"Ruqi Li , Yurong Song , Min Li , Hongbo Qu , Guo-Ping Jiang","doi":"10.1016/j.matcom.2024.10.042","DOIUrl":"10.1016/j.matcom.2024.10.042","url":null,"abstract":"<div><div>To analyze and predict the evolution of contagion dynamics, fractional derivative modeling has emerged as an important technique. However, inferring the dynamical structure of fractional-order models with high degrees of freedom poses a challenge. In this paper, to elucidate the spreading mechanism and non-local properties of disease evolution, we propose a novel fractional-order SEIHDR epidemiological model with variable parameters, incorporating fractional derivatives in the Caputo sense. We compute the basic reproduction number by the next-generation matrix and establish local and global stability conditions based on this reproduction number. By using the fractional Adams–Bashforth method, we validate dynamical behaviors at different equilibrium points in both autonomous and non-autonomous scenarios, while qualitatively analyze the effects of fractional order on the dynamics. To effectively address the inverse problem of the proposed fractional SEIHDR model, we construct a fractional Physics-Informed Neural Network framework to simultaneously infer time-dependent parameters, fractional orders, and state components. Graphical results based on the COVID-19 pandemic data from Canada demonstrate the effectiveness of the proposed framework.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"230 ","pages":"Pages 1-19"},"PeriodicalIF":4.4,"publicationDate":"2024-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142659321","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}
Pub Date : 2024-10-31DOI: 10.1016/j.matcom.2024.10.028
Deepika Sharma, Randheer Singh
In this manuscript, a mathematical model describing isentropic two-phase real modified Chaplygin flow with a non-constant source term has been considered. The model governed by the system of partial differential equations (PDEs) is reduced into an equivalent system of ordinary differential equations (ODEs) via Lie-symmetry analysis. The transport equations for the characteristic shock and acceleration wave are derived to analyze their evolutionary behavior and solved numerically along with the system of ODEs. Special attention is devoted to investigate the effects of non-idealness and source term on the progression of characteristic shock and acceleration wave. Moreover, the amplitude of the reflected wave, transmitted wave and jump in the acceleration of shock, generated from the interaction of characteristic with acceleration wave, are computed.
{"title":"Interaction of an acceleration wave with a characteristic shock in two-phase real modified Chaplygin model containing a variable source term","authors":"Deepika Sharma, Randheer Singh","doi":"10.1016/j.matcom.2024.10.028","DOIUrl":"10.1016/j.matcom.2024.10.028","url":null,"abstract":"<div><div>In this manuscript, a mathematical model describing isentropic two-phase real modified Chaplygin flow with a non-constant source term has been considered. The model governed by the system of partial differential equations (PDEs) is reduced into an equivalent system of ordinary differential equations (ODEs) via Lie-symmetry analysis. The transport equations for the characteristic shock and acceleration wave are derived to analyze their evolutionary behavior and solved numerically along with the system of ODEs. Special attention is devoted to investigate the effects of non-idealness and source term on the progression of characteristic shock and acceleration wave. Moreover, the amplitude of the reflected wave, transmitted wave and jump in the acceleration of shock, generated from the interaction of characteristic with acceleration wave, are computed.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"230 ","pages":"Pages 53-67"},"PeriodicalIF":4.4,"publicationDate":"2024-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142659323","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}
Pub Date : 2024-10-29DOI: 10.1016/j.matcom.2024.10.034
Gaetano Settembre , Nicolò Taggio , Nicoletta Del Buono , Flavia Esposito , Paola Di Lauro , Antonello Aiello
Wildfires are becoming increasingly common events, and studying them, monitoring their effects, and assessing the damage they produce, is crucial for planning recovery efforts. The new generation of hyperspectral satellite sensors can provide highly detailed spectral information directly related to materials on the Earth’s surface, allowing the detection of potential changes in monitored areas. These instruments allow the detection of even small land changes, such as those in homogeneous areas of interest. Unlike binary change detection mechanisms that can only produce a map of changes in observed areas, our goal is to provide a mathematical framework to construct semantic maps of land change before and after an impactful event. This feature is particularly useful for monitoring land use and land cover (LULC), agriculture, and damage assessment in fire-affected areas. This paper presents a framework for remote sensing change analysis between bitemporal hyperspectral images, namely SemBLCC, whose core is a hierarchical clustering algorithm based on a rank-two nonnegative matrix factorization. SemBLCC is able to explicitly model the semantic “from-to” transitions between the two involved hyperspectral images, thanks to new spectral libraries specifically designed for the new data acquired by PRISMA (PRecursore IperSpettrale della Missione Applicativa) satellite. SemBLCC has been successfully used to produce LULC change maps of fire-affected areas, allowing accurate assessment of fire damage.
{"title":"A land cover change framework analyzing wildfire-affected areas in bitemporal PRISMA hyperspectral images","authors":"Gaetano Settembre , Nicolò Taggio , Nicoletta Del Buono , Flavia Esposito , Paola Di Lauro , Antonello Aiello","doi":"10.1016/j.matcom.2024.10.034","DOIUrl":"10.1016/j.matcom.2024.10.034","url":null,"abstract":"<div><div>Wildfires are becoming increasingly common events, and studying them, monitoring their effects, and assessing the damage they produce, is crucial for planning recovery efforts. The new generation of hyperspectral satellite sensors can provide highly detailed spectral information directly related to materials on the Earth’s surface, allowing the detection of potential changes in monitored areas. These instruments allow the detection of even small land changes, such as those in homogeneous areas of interest. Unlike binary change detection mechanisms that can only produce a map of changes in observed areas, our goal is to provide a mathematical framework to construct semantic maps of land change before and after an impactful event. This feature is particularly useful for monitoring land use and land cover (LULC), agriculture, and damage assessment in fire-affected areas. This paper presents a framework for remote sensing change analysis between bitemporal hyperspectral images, namely SemBLCC, whose core is a hierarchical clustering algorithm based on a rank-two nonnegative matrix factorization. SemBLCC is able to explicitly model the semantic “from-to” transitions between the two involved hyperspectral images, thanks to new spectral libraries specifically designed for the new data acquired by PRISMA (PRecursore IperSpettrale della Missione Applicativa) satellite. SemBLCC has been successfully used to produce LULC change maps of fire-affected areas, allowing accurate assessment of fire damage.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"229 ","pages":"Pages 855-866"},"PeriodicalIF":4.4,"publicationDate":"2024-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142659628","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}
Pub Date : 2024-10-28DOI: 10.1016/j.matcom.2024.10.033
F. El Mokhtari , M. Lamnii , D. Barrera
This paper focuses on the approximation of solutions of second kind Fredholm integral equations using non-uniform spline quasi-interpolation. Our aim is to determine the most effective non-uniform partition that provides an optimal numerical solution to the integral equation. To achieve this, we introduce a solution approach based on genetic algorithms, using right approximation of the integral equation’s kernel. We present some numerical examples to show the method’s performance.
{"title":"A genetic algorithm approach based on spline quasi-interpolation for solving Fredholm integral equations","authors":"F. El Mokhtari , M. Lamnii , D. Barrera","doi":"10.1016/j.matcom.2024.10.033","DOIUrl":"10.1016/j.matcom.2024.10.033","url":null,"abstract":"<div><div>This paper focuses on the approximation of solutions of second kind Fredholm integral equations using non-uniform spline quasi-interpolation. Our aim is to determine the most effective non-uniform partition that provides an optimal numerical solution to the integral equation. To achieve this, we introduce a solution approach based on genetic algorithms, using right approximation of the integral equation’s kernel. We present some numerical examples to show the method’s performance.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"229 ","pages":"Pages 725-742"},"PeriodicalIF":4.4,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142579063","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}
Pub Date : 2024-10-28DOI: 10.1016/j.matcom.2024.10.016
Dongping He , Jaume Llibre
In this paper we study the limit cycles which bifurcate from the periodic orbits of the quadratic uniform isochronous center , , when this center is perturbed inside the class of all discontinuous piecewise quadratic polynomial differential systems in the plane with two pieces separated by a non-regular line of discontinuity, which is formed by two rays starting from the origin and forming an angle . Using the Chebyshev theory we prove that the maximum number of hyperbolic limit cycles which can bifurcate from these periodic orbits is exactly 8 using the averaging theory of first order. For this class of discontinuous piecewise differential systems we obtain three more limit cycles than the line of discontinuity is regular, i.e., the case of where the two rays form an angle .
{"title":"Limit cycles in a class of planar discontinuous piecewise quadratic differential systems with a non-regular line of discontinuity (I)","authors":"Dongping He , Jaume Llibre","doi":"10.1016/j.matcom.2024.10.016","DOIUrl":"10.1016/j.matcom.2024.10.016","url":null,"abstract":"<div><div>In this paper we study the limit cycles which bifurcate from the periodic orbits of the quadratic uniform isochronous center <span><math><mrow><mover><mrow><mi>x</mi></mrow><mrow><mo>̇</mo></mrow></mover><mo>=</mo><mo>−</mo><mi>y</mi><mo>+</mo><mi>x</mi><mi>y</mi></mrow></math></span>, <span><math><mrow><mover><mrow><mi>y</mi></mrow><mrow><mo>̇</mo></mrow></mover><mo>=</mo><mi>x</mi><mo>+</mo><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math></span>, when this center is perturbed inside the class of all discontinuous piecewise quadratic polynomial differential systems in the plane with two pieces separated by a non-regular line of discontinuity, which is formed by two rays starting from the origin and forming an angle <span><math><mrow><mi>α</mi><mo>=</mo><mi>π</mi><mo>/</mo><mn>2</mn></mrow></math></span>. Using the Chebyshev theory we prove that the maximum number of hyperbolic limit cycles which can bifurcate from these periodic orbits is exactly 8 using the averaging theory of first order. For this class of discontinuous piecewise differential systems we obtain three more limit cycles than the line of discontinuity is regular, i.e., the case of where the two rays form an angle <span><math><mrow><mi>α</mi><mo>=</mo><mi>π</mi></mrow></math></span>.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"229 ","pages":"Pages 743-757"},"PeriodicalIF":4.4,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142579069","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}
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