Advances in continuous and discrete models最新文献

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Computing confined elasticae 计算受限弹性
Advances in continuous and discrete models Pub Date : 2022-03-17 DOI: 10.1186/s13662-022-03731-7
S. Bartels, Pascal Weyer
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引用次数: 1
Convergence of second-order in time numerical discretizations for the evolution Navier-Stokes equations 演化Navier-Stokes方程二阶时间数值离散化的收敛性
Advances in continuous and discrete models Pub Date : 2022-03-01 DOI: 10.1186/s13662-022-03736-2
L. Berselli, S. Spirito
{"title":"Convergence of second-order in time numerical discretizations for the evolution Navier-Stokes equations","authors":"L. Berselli, S. Spirito","doi":"10.1186/s13662-022-03736-2","DOIUrl":"https://doi.org/10.1186/s13662-022-03736-2","url":null,"abstract":"","PeriodicalId":72091,"journal":{"name":"Advances in continuous and discrete models","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49582853","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Partial asymptotic stability of neutral pantograph stochastic differential equations with Markovian switching 具有马尔可夫切换的中性受电弓随机微分方程的部分渐近稳定性
Advances in continuous and discrete models Pub Date : 2022-02-25 DOI: 10.1186/s13662-022-03692-x
Lassaad Mchiri, T. Caraballo, Mohamed Rhaima
{"title":"Partial asymptotic stability of neutral pantograph stochastic differential equations with Markovian switching","authors":"Lassaad Mchiri, T. Caraballo, Mohamed Rhaima","doi":"10.1186/s13662-022-03692-x","DOIUrl":"https://doi.org/10.1186/s13662-022-03692-x","url":null,"abstract":"","PeriodicalId":72091,"journal":{"name":"Advances in continuous and discrete models","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"65777571","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Geometric properties of the meromorphic functions class through special functions associated with a linear operator 通过与线性算子相关的特殊函数研究亚纯函数类的几何性质
Advances in continuous and discrete models Pub Date : 2022-02-19 DOI: 10.1186/s13662-022-03691-y
F. Ghanim, H. Al‐Janaby, O. Bazighifan
{"title":"Geometric properties of the meromorphic functions class through special functions associated with a linear operator","authors":"F. Ghanim, H. Al‐Janaby, O. Bazighifan","doi":"10.1186/s13662-022-03691-y","DOIUrl":"https://doi.org/10.1186/s13662-022-03691-y","url":null,"abstract":"","PeriodicalId":72091,"journal":{"name":"Advances in continuous and discrete models","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"65777549","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
The Lax pair structure for the spin Benjamin–Ono equation 自旋Benjamin-Ono方程的Lax对结构
Advances in continuous and discrete models Pub Date : 2022-02-16 DOI: 10.1186/s13662-023-03768-2
P. G'erard
{"title":"The Lax pair structure for the spin Benjamin–Ono equation","authors":"P. G'erard","doi":"10.1186/s13662-023-03768-2","DOIUrl":"https://doi.org/10.1186/s13662-023-03768-2","url":null,"abstract":"","PeriodicalId":72091,"journal":{"name":"Advances in continuous and discrete models","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48478282","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
Analytical analysis of fractional-order sequential hybrid system with numerical application 分数阶序列混合系统的解析分析及其数值应用
Advances in continuous and discrete models Pub Date : 2022-02-02 DOI: 10.1186/s13662-022-03685-w
Aziz Khan, Z. Khan, T. Abdeljawad, H. Khan
{"title":"Analytical analysis of fractional-order sequential hybrid system with numerical application","authors":"Aziz Khan, Z. Khan, T. Abdeljawad, H. Khan","doi":"10.1186/s13662-022-03685-w","DOIUrl":"https://doi.org/10.1186/s13662-022-03685-w","url":null,"abstract":"","PeriodicalId":72091,"journal":{"name":"Advances in continuous and discrete models","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48999807","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 20
Application of Legendre polynomials based neural networks for the analysis of heat and mass transfer of a non-Newtonian fluid in a porous channel 基于勒让德多项式的神经网络在多孔通道中非牛顿流体传热传质分析中的应用
Advances in continuous and discrete models Pub Date : 2022-01-22 DOI: 10.1186/s13662-022-03676-x
N. A. Khan, M. Sulaiman, P. Kumam, F. Alarfaj
{"title":"Application of Legendre polynomials based neural networks for the analysis of heat and mass transfer of a non-Newtonian fluid in a porous channel","authors":"N. A. Khan, M. Sulaiman, P. Kumam, F. Alarfaj","doi":"10.1186/s13662-022-03676-x","DOIUrl":"https://doi.org/10.1186/s13662-022-03676-x","url":null,"abstract":"","PeriodicalId":72091,"journal":{"name":"Advances in continuous and discrete models","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"65777032","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
Stochastic optimal control with random coefficients and associated stochastic Hamilton–Jacobi–Bellman equations 随机系数随机最优控制及相关随机Hamilton-Jacobi-Bellman方程
Advances in continuous and discrete models Pub Date : 2022-01-14 DOI: 10.1186/s13662-021-03674-5
Jun Moon
{"title":"Stochastic optimal control with random coefficients and associated stochastic Hamilton–Jacobi–Bellman equations","authors":"Jun Moon","doi":"10.1186/s13662-021-03674-5","DOIUrl":"https://doi.org/10.1186/s13662-021-03674-5","url":null,"abstract":"","PeriodicalId":72091,"journal":{"name":"Advances in continuous and discrete models","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"65776934","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A physics-informed neural network to model COVID-19 infection and hospitalization scenarios. 用于模拟 COVID-19 感染和住院情况的物理信息神经网络。
IF 2.3
Advances in continuous and discrete models Pub Date : 2022-01-01 Epub Date: 2022-10-27 DOI: 10.1186/s13662-022-03733-5
Sarah Berkhahn, Matthias Ehrhardt
{"title":"A physics-informed neural network to model COVID-19 infection and hospitalization scenarios.","authors":"Sarah Berkhahn, Matthias Ehrhardt","doi":"10.1186/s13662-022-03733-5","DOIUrl":"10.1186/s13662-022-03733-5","url":null,"abstract":"<p><p>In this paper, we replace the standard numerical approach of estimating parameters in a mathematical model using numerical solvers for differential equations with a physics-informed neural network (PINN). This neural network requires a sequence of time instances as direct input of the network and the numbers of susceptibles, vaccinated, infected, hospitalized, and recovered individuals per time instance to learn certain parameters of the underlying model, which are used for the loss calculations. The established model is an extended susceptible-infected-recovered (SIR) model in which the transitions between disease-related population groups, called compartments, and the physical laws of epidemic transmission dynamics are expressed by a system of ordinary differential equations (ODEs). The system of ODEs and its time derivative are included in the residual loss function of the PINN in addition to the data error between the current network output and the time series data of the compartment sizes. Further, we illustrate how this PINN approach can also be used for differential equation-based models such as the proposed extended SIR model, called SVIHR model. In a validation process, we compare the performance of the PINN with results obtained with the numerical technique of non-standard finite differences (NSFD) in generating future COVID-19 scenarios based on the parameters identified by the PINN. The used training data set covers the time between the outbreak of the pandemic in Germany and the last week of the year 2021. We obtain a two-step or hybrid approach, as the PINN is then used to generate a future COVID-19 outbreak scenario describing a possibly next pandemic wave. The week at which the prediction starts is chosen in mid-April 2022.</p>","PeriodicalId":72091,"journal":{"name":"Advances in continuous and discrete models","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9612630/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"40461900","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
Dynamics analysis and optimal control of SIVR epidemic model with incomplete immunity. 具有不完全免疫力的 SIVR 流行模型的动力学分析与优化控制
IF 2.3
Advances in continuous and discrete models Pub Date : 2022-01-01 Epub Date: 2022-07-18 DOI: 10.1186/s13662-022-03723-7
Yiming Liu, Shuang Jian, Jianguo Gao
{"title":"Dynamics analysis and optimal control of SIVR epidemic model with incomplete immunity.","authors":"Yiming Liu, Shuang Jian, Jianguo Gao","doi":"10.1186/s13662-022-03723-7","DOIUrl":"10.1186/s13662-022-03723-7","url":null,"abstract":"<p><p>In this paper, we establish an SIVR model with diffusion, spatially heterogeneous, latent infection, and incomplete immunity in the Neumann boundary condition. Firstly, the threshold dynamic behavior of the model is proved by using the operator semigroup method, the well-posedness of the solution and the basic reproduction number <math><msub><mi>ℜ</mi> <mn>0</mn></msub> </math> are given. When <math><msub><mi>ℜ</mi> <mn>0</mn></msub> <mo><</mo> <mn>1</mn></math> , the disease-free equilibrium is globally asymptotically stable, the disease will be extinct; when <math><msub><mi>ℜ</mi> <mn>0</mn></msub> <mo>></mo> <mn>1</mn></math> , the epidemic equilibrium is globally asymptotically stable, the disease will persist with probability one. Then, we introduce the patient's treatment into the system as the control parameter, and the optimal control of the system is discussed by applying the Hamiltonian function and the adjoint equation. Finally, the theoretical results are verified by numerical simulation.</p>","PeriodicalId":72091,"journal":{"name":"Advances in continuous and discrete models","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9294857/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"40534598","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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