Computational and Mathematical Methods最新文献

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The Rate of Convergence of the SOR Method in the Positive Semidefinite Case 正半定情况下SOR方法的收敛速度
IF 0.9
Computational and Mathematical Methods Pub Date : 2022-03-02 DOI: 10.1155/2022/6143444
Achiya Dax
{"title":"The Rate of Convergence of the SOR Method in the Positive Semidefinite Case","authors":"Achiya Dax","doi":"10.1155/2022/6143444","DOIUrl":"10.1155/2022/6143444","url":null,"abstract":"<div>\u0000 <p>In this paper, we derive upper bounds that characterize the rate of convergence of the SOR method for solving a linear system of the form <i>G</i><i>x</i> = <i>b</i>, where <i>G</i> is a real symmetric positive semidefinite <i>n</i> × <i>n</i> matrix. The bounds are given in terms of the condition number of <i>G</i>, which is the ratio <i>κ</i> = <i>α</i>/<i>β</i>, where <i>α</i> is the largest eigenvalue of <i>G</i> and <i>β</i> is the smallest nonzero eigenvalue of <i>G</i>. Let <i>H</i> denote the related iteration matrix. Then, since <i>G</i> has a zero eigenvalue, the spectral radius of <i>H</i> equals 1, and the rate of convergence is determined by the size of <i>η</i>, the largest eigenvalue of <i>H</i> whose modulus differs from 1. The bound has the form |<i>η</i>|<sup>2</sup> ≤ 1 − 1/(<i>κ</i><i>c</i>), where <i>c</i> = 2 + log<sub>2</sub><i>n</i>. The main consequence from this bound is that small condition number forces fast convergence while large condition number allows slow convergence.</p>\u0000 </div>","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"2022 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/2022/6143444","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84729968","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Effect of General Cross-Immunity Protection and Antibody-Dependent Enhancement in Dengue Dynamics 一般交叉免疫保护和抗体依赖性增强在登革热动力学中的作用
IF 0.9
Computational and Mathematical Methods Pub Date : 2022-02-13 DOI: 10.1155/2022/2074325
Vanessa Steindorf, Sergio Oliva, Jianhong Wu, Maíra Aguiar
{"title":"Effect of General Cross-Immunity Protection and Antibody-Dependent Enhancement in Dengue Dynamics","authors":"Vanessa Steindorf,&nbsp;Sergio Oliva,&nbsp;Jianhong Wu,&nbsp;Maíra Aguiar","doi":"10.1155/2022/2074325","DOIUrl":"10.1155/2022/2074325","url":null,"abstract":"<div>\u0000 <p>A mathematical model to describe the dynamic of a multiserotype infectious disease at the population level is studied. Applied to dengue fever epidemiology, we analyse a mathematical model with time delay to describe the cross-immunity protection period, including a key parameter for the antibody-dependent enhancement (ADE) effect, the well-known features of dengue fever infection. Numerical experiments are performed to show the stability of the coexistence equilibrium, which is completely determined by the basic reproduction number and by the invasion reproduction number, as well as the bifurcation structures for different scenarios of dengue fever transmission in a population. The model shows a rich dynamical behavior, from fixed points and periodic oscillations up to chaotic behaviour with complex attractors.</p>\u0000 </div>","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"2022 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/2022/2074325","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84647218","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Spatially Extended SHAR Epidemiological Framework of Infectious Disease Transmission 传染病传播的空间扩展share流行病学框架
IF 0.9
Computational and Mathematical Methods Pub Date : 2022-02-13 DOI: 10.1155/2022/3304532
Damián Knopoff, Nicole Cusimano, Nico Stollenwerk, Maíra Aguiar
{"title":"Spatially Extended SHAR Epidemiological Framework of Infectious Disease Transmission","authors":"Damián Knopoff,&nbsp;Nicole Cusimano,&nbsp;Nico Stollenwerk,&nbsp;Maíra Aguiar","doi":"10.1155/2022/3304532","DOIUrl":"10.1155/2022/3304532","url":null,"abstract":"<div>\u0000 <p>Mathematical models play an important role in epidemiology. The inclusion of a spatial component in epidemiological models is especially important to understand and address many relevant ecological and public health questions, e.g., when wanting to differentiate transmission patterns across geographical regions or when considering spatially heterogeneous intervention measures. However, the introduction of spatial effects can have significant consequences on the observed model dynamics and hence must be carefully analyzed and interpreted. Cellular automata epidemiological models typically rely on simplified computational grids but can provide valuable insight into the spatial dynamics of transmission within a population by suitably accounting for the connections between individuals in the considered community. In this paper, we describe a stochastic cellular automata disease model based on an extension of the traditional Susceptible-Infected-Recovered (SIR) compartmentalization of the population, namely, the Susceptible-Hospitalized-Asymptomatic-Recovered (SHAR) formulation, in which infected individuals either present a severe form of the disease, thus requiring hospitalization, or belong to the so-called mild/asymptomatic class. The critical transmission threshold is derived analytically in the nonspatial SHAR formulation, and this generalizes previously obtained theoretical results for the SIR model. We present simulation results discussing the effect of key model parameters and of spatial correlations on model outputs and propose an algorithm for tracking the evolution of infection clusters within the considered population. Focusing on the role of import and criticality on the overall dynamics, we conclude that the current spatial setting increases the critical transmission threshold in comparison to the nonspatial model.</p>\u0000 </div>","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"2022 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/2022/3304532","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79784711","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Cell-Centered Semi-Lagrangian Finite Volume Method for Solving Two-Dimensional Coupled Burgers’ Equations 求解二维耦合Burgers方程的半拉格朗日有限体积法
IF 0.9
Computational and Mathematical Methods Pub Date : 2022-02-13 DOI: 10.1155/2022/8192192
Ilham Asmouh, Mofdi El-Amrani, Mohammed Seaid, Naji Yebari
{"title":"A Cell-Centered Semi-Lagrangian Finite Volume Method for Solving Two-Dimensional Coupled Burgers’ Equations","authors":"Ilham Asmouh,&nbsp;Mofdi El-Amrani,&nbsp;Mohammed Seaid,&nbsp;Naji Yebari","doi":"10.1155/2022/8192192","DOIUrl":"10.1155/2022/8192192","url":null,"abstract":"<div>\u0000 <p>A cell-centered finite volume semi-Lagrangian method is presented for the numerical solution of two-dimensional coupled Burgers’ problems on unstructured triangular meshes. The method combines a modified method of characteristics for the time integration and a cell-centered finite volume for the space discretization. The new method belongs to fractional-step algorithms for which the convection and the viscous parts in the coupled Burgers’ problems are treated separately. The crucial step of interpolation in the convection step is performed using two local procedures accounting for the element where the departure point is located. The resulting semidiscretized system is then solved using a third-order explicit Runge-Kutta scheme. In contrast to the Eulerian-based methods, we apply the new method for each time step along the characteristic curves instead of the time direction. The performance of the current method is verified using different examples for coupled Burgers’ problems with known analytical solutions. We also apply the method for simulation of an example of coupled Burgers’ flows in a complex geometry. In these test problems, the new cell-centered finite volume semi-Lagrangian method demonstrates its ability to accurately resolve the two-dimensional coupled Burgers’ problems.</p>\u0000 </div>","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"2022 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/2022/8192192","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84834098","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Study of a Set of Symmetric Temporal Transformations for the Study of the Orbital Motion 研究轨道运动的一组对称时间变换的研究
IF 0.9
Computational and Mathematical Methods Pub Date : 2022-02-13 DOI: 10.1155/2022/9037530
José Antonio López Ortí, Vicente Agost Gómez, Miguel Barreda Rochera
{"title":"Study of a Set of Symmetric Temporal Transformations for the Study of the Orbital Motion","authors":"José Antonio López Ortí,&nbsp;Vicente Agost Gómez,&nbsp;Miguel Barreda Rochera","doi":"10.1155/2022/9037530","DOIUrl":"10.1155/2022/9037530","url":null,"abstract":"<div>\u0000 <p>The main goal of this paper is to define a new one-parametric family of symmetric temporal transformations with respect to the ellipse. This new family contains as a particular case the eccentric anomaly, the regularized length of arc, and the elliptic anomaly. This family is a particular case of the biparametric family of anomalies introduced by the authors in 2016. The biparametric family comprises the most common anomalies used in the study of the two-body problem. Two approaches of this work have been taken. The first one involves the study of the analytical properties of the symmetric family of anomalies. The second approach explores the improvement of the numerical integration methods when the natural time is replaced by an anomaly of this family.</p>\u0000 </div>","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"2022 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/2022/9037530","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74594850","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Deterministic and Stochastic Dynamics of COVID-19: The Case Study of Italy and Spain COVID-19的确定性和随机动力学:以意大利和西班牙为例
IF 0.9
Computational and Mathematical Methods Pub Date : 2022-02-13 DOI: 10.1155/2022/5780719
Akhil Kumar Srivastav, Nico Stollenwerk, Maíra Aguiar
{"title":"Deterministic and Stochastic Dynamics of COVID-19: The Case Study of Italy and Spain","authors":"Akhil Kumar Srivastav,&nbsp;Nico Stollenwerk,&nbsp;Maíra Aguiar","doi":"10.1155/2022/5780719","DOIUrl":"10.1155/2022/5780719","url":null,"abstract":"<div>\u0000 <p>In December 2019, a severe respiratory syndrome (COVID-19) caused by a new coronavirus (SARS-CoV-2) was identified in China and spread rapidly around the globe. COVID-19 was declared a pandemic by the World Health Organization (WHO) in March 2020. With eventually substantial global underestimation, more than 225 million cases were confirmed by the end of August 2021, counting more than 4.5 million deaths. COVID-19 symptoms range from mild (or no symptoms) to severe illness, with disease severity and death occurring according to a hierarchy of risks, with age and preexisting health conditions enhancing the risks of disease severity manifestation. In this paper, a mathematical model for COVID-19 transmission is proposed and analyzed. The model stratifies the studied population into two groups, older and younger. Applied to the COVID-19 outbreaks in Spain and in Italy, we find the disease-free equilibrium and the basic reproduction number for each case study. A sensitivity analysis to identify the key parameters which influence the basic reproduction number, and hence regulate the transmission dynamics of COVID-19, is also performed. Finally, the model is extended to its stochastic counterpart to encapsulate the variation or uncertainty found in the transmissibility of the disease. We observe the variability of the infectious population finding its distribution at a given time, demonstrating that for small populations, stochasticity will play an important role.</p>\u0000 </div>","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"2022 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/2022/5780719","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81061582","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Improved Shape Parameter Estimation for the Three-Parameter Log-Logistic Distribution 三参数logistic分布的改进形状参数估计
IF 0.9
Computational and Mathematical Methods Pub Date : 2022-02-13 DOI: 10.1155/2022/8400130
Ayana Mateus, Frederico Caeiro
{"title":"Improved Shape Parameter Estimation for the Three-Parameter Log-Logistic Distribution","authors":"Ayana Mateus,&nbsp;Frederico Caeiro","doi":"10.1155/2022/8400130","DOIUrl":"10.1155/2022/8400130","url":null,"abstract":"<div>\u0000 <p>The log-logistic distribution is widely used in different fields of study such as survival analysis, hydrology, insurance, and economics. Recently, Ahsanullah and Alzaatreh studied the best linear unbiased estimators for the location and the scale parameters of the three-parameter log-logistic model. The same authors also propose a shift-invariant Hill estimator for the unknown shape parameter. In this work, we propose a new estimation method for the shape parameter. We derive its nondegenerate asymptotic behaviour and analyse its finite sample performance through a Monte Carlo simulation study. To have precise estimates, we present a method for selecting the threshold. To illustrate the improvement achieved, efficiency comparisons are also provided.</p>\u0000 </div>","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"2022 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/2022/8400130","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81981386","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Numerical Approach for Singularly Perturbed Nonlinear Delay Differential Equations Using a Trigonometric Spline 奇异摄动非线性时滞微分方程的三角样条数值解法
IF 0.9
Computational and Mathematical Methods Pub Date : 2022-02-13 DOI: 10.1155/2022/8338661
M. Lalu, K. Phaneendra
{"title":"A Numerical Approach for Singularly Perturbed Nonlinear Delay Differential Equations Using a Trigonometric Spline","authors":"M. Lalu,&nbsp;K. Phaneendra","doi":"10.1155/2022/8338661","DOIUrl":"10.1155/2022/8338661","url":null,"abstract":"<div>\u0000 <p>In this paper, a computational procedure for solving singularly perturbed nonlinear delay differentiation equations (SPNDDEs) is proposed. Initially, the SPNDDE is reduced into a series of singularly perturbed linear delay differential equations (SPLDDEs) using the quasilinearization technique. A trigonometric spline approach is suggested to solve the sequence of SPLDDEs. Convergence of the method is addressed. The efficiency and applicability of the proposed method are demonstrated by the numerical examples.</p>\u0000 </div>","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"2022 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/2022/8338661","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82701588","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A New Probability Model Based on a Coherent System with Applications 一种新的基于相干系统的概率模型及其应用
IF 0.9
Computational and Mathematical Methods Pub Date : 2022-02-13 DOI: 10.1155/2022/8564465
Christophe Chesneau, Hassan S. Bakouch, Bilal A. Para, Mohammad H. Poursaeed
{"title":"A New Probability Model Based on a Coherent System with Applications","authors":"Christophe Chesneau,&nbsp;Hassan S. Bakouch,&nbsp;Bilal A. Para,&nbsp;Mohammad H. Poursaeed","doi":"10.1155/2022/8564465","DOIUrl":"10.1155/2022/8564465","url":null,"abstract":"<div>\u0000 <p>The notion of a coherent system allows us to formalize how the random lifetime of the system is connected to the random lifetimes of its components. These connections are also generators of new pliant distributions, being those of various mixes of minimum and maximum of random variables. In this paper, a new four-parameter lifetime probability distribution is introduced by using the notion of a coherent system. Its structural properties are assessed and evaluated, including the analytical study of its main functions, stochastic dominance results, moments, and moment generating function. The proposed distribution, in particular, is proving to be efficient at fitting data with slight negative skewness and platykurtic as well as leptokurtic nature. This is illustrated by the analysis of three relevant real-life data sets, two in reliability and another in production, exhibiting the significance of the introduced model in comparison to various well-known models in statistical literature.</p>\u0000 </div>","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"2022 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/2022/8564465","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84702125","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Deep Brain Stimulation with a Computational Model for the Cortex-Thalamus-Basal-Ganglia System and Network Dynamics of Neurological Disorders 深部脑刺激与皮层-丘脑-基底神经节系统的计算模型和神经系统疾病的网络动力学
IF 0.9
Computational and Mathematical Methods Pub Date : 2022-02-13 DOI: 10.1155/2022/8998150
Hina Shaheen, Roderick Melnik
{"title":"Deep Brain Stimulation with a Computational Model for the Cortex-Thalamus-Basal-Ganglia System and Network Dynamics of Neurological Disorders","authors":"Hina Shaheen,&nbsp;Roderick Melnik","doi":"10.1155/2022/8998150","DOIUrl":"10.1155/2022/8998150","url":null,"abstract":"<div>\u0000 <p>Deep brain stimulation (DBS) can alleviate the movement disorders like Parkinson’s disease (PD). Indeed, it is known that aberrant beta (13-30 Hz) oscillations and the loss of dopaminergic neurons in the basal ganglia-thalamus (BGTH) and cortex characterize the akinesia symptoms of PD. However, the relevant biophysical mechanism behind this process still remains unclear. Based on the prior striatal inhibitory model, we propose an extended BGTH model incorporating medium spine neurons (MSNs) and fast-spiking interneurons (FSIs) along with the effect of DBS. We are focusing in this paper on an open-loop DBS mode, where the stimulation parameters stay constant independent of variations in the disease state, and modifications of parameters rely mainly on trial and error of medical experts. Additionally, we propose a novel combined model of the cerebellar-basal-ganglia thalamocortical network, MSNs, and FSIs and show new results that indicate that Parkinsonian oscillations in the beta-band frequency range emerge from the dynamics of such a network. Our model predicts that DBS can be used to suppress beta oscillations in globus pallidus pars interna (GPi) neurons. This research will help our better understanding of the changes in the brain activity caused by DBS, providing new insight for studying PD in the future.</p>\u0000 </div>","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"2022 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/2022/8998150","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82439332","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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