Advances in continuous and discrete models最新文献

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On three-term conjugate gradient method for optimization problems with applications on COVID-19 model and robotic motion control. 三项共轭梯度法在COVID-19模型和机器人运动控制中的应用

Q1 MATHEMATICS

Advances in continuous and discrete models

Pub Date : 2022-01-01 DOI: 10.1186/s13662-021-03638-9

Ibrahim Mohammed Sulaiman, Maulana Malik, Aliyu Muhammed Awwal, Poom Kumam, Mustafa Mamat, Shadi Al-Ahmad

The three-term conjugate gradient (CG) algorithms are among the efficient variants of CG algorithms for solving optimization models. This is due to their simplicity and low memory requirements. On the other hand, the regression model is one of the statistical relationship models whose solution is obtained using one of the least square methods including the CG-like method. In this paper, we present a modification of a three-term conjugate gradient method for unconstrained optimization models and further establish the global convergence under inexact line search. The proposed method was extended to formulate a regression model for the novel coronavirus (COVID-19). The study considers the globally infected cases from January to October 2020 in parameterizing the model. Preliminary results have shown that the proposed method is promising and produces efficient regression model for COVID-19 pandemic. Also, the method was extended to solve a motion control problem involving a two-joint planar robot.

三项共轭梯度(CG)算法是求解优化模型的一种有效的CG算法。这是由于它们的简单性和低内存需求。另一方面，回归模型是一种统计关系模型，其解是使用最小二乘法之一，包括类cg方法。本文对无约束优化模型的一种三项共轭梯度法进行了改进，进一步建立了非精确直线搜索下的全局收敛性。将该方法扩展到新型冠状病毒(COVID-19)的回归模型。该研究考虑了2020年1月至10月全球感染病例的参数化模型。初步结果表明，该方法具有较好的应用前景，能够建立有效的COVID-19大流行回归模型。并将该方法推广到两关节平面机器人的运动控制问题。

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引用次数: 17

Uniform convergence guarantees for the deep Ritz method for nonlinear problems. 非线性问题的深里兹方法的一致收敛保证。

Q1 MATHEMATICS

Advances in continuous and discrete models

Pub Date : 2022-01-01 Epub Date: 2022-07-15 DOI: 10.1186/s13662-022-03722-8

Patrick Dondl, Johannes Müller, Marius Zeinhofer

We provide convergence guarantees for the Deep Ritz Method for abstract variational energies. Our results cover nonlinear variational problems such as the p-Laplace equation or the Modica-Mortola energy with essential or natural boundary conditions. Under additional assumptions, we show that the convergence is uniform across bounded families of right-hand sides.

我们提供了抽象变分能量的深里兹方法的收敛性保证。我们的结果涵盖了非线性变分问题，如p-拉普拉斯方程或具有本质或自然边界条件的Modica-Mortola能量。在附加的假设下，我们证明了收敛性在右边有界族上是一致的。

引用次数: 7

A delayed plant disease model with Caputo fractional derivatives. 带有卡普托分数导数的延迟植物病害模型。

IF 2.3 Q1 MATHEMATICS

Advances in continuous and discrete models

Pub Date : 2022-01-01 Epub Date: 2022-01-29 DOI: 10.1186/s13662-022-03684-x

Pushpendra Kumar, Dumitru Baleanu, Vedat Suat Erturk, Mustafa Inc, V Govindaraj

We analyze a time-delay Caputo-type fractional mathematical model containing the infection rate of Beddington-DeAngelis functional response to study the structure of a vector-borne plant epidemic. We prove the unique global solution existence for the given delay mathematical model by using fixed point results. We use the Adams-Bashforth-Moulton P-C algorithm for solving the given dynamical model. We give a number of graphical interpretations of the proposed solution. A number of novel results are demonstrated from the given practical and theoretical observations. By using 3-D plots we observe the variations in the flatness of our plots when the fractional order varies. The role of time delay on the proposed plant disease dynamics and the effects of infection rate in the population of susceptible and infectious classes are investigated. The main motivation of this research study is examining the dynamics of the vector-borne epidemic in the sense of fractional derivatives under memory effects. This study is an example of how the fractional derivatives are useful in plant epidemiology. The application of Caputo derivative with equal dimensionality includes the memory in the model, which is the main novelty of this study.

我们分析了一个包含贝丁顿-德安吉利斯函数反应感染率的时延卡普托型分数数学模型，以研究媒介传播植物流行病的结构。我们利用定点结果证明了给定延迟数学模型的唯一全局解存在性。我们使用 Adams-Bashforth-Moulton P-C 算法求解给定的动力学模型。我们对提出的解给出了一些图形解释。从给定的实践和理论观察中，我们展示了一些新的结果。通过使用三维图，我们观察到当分数阶数变化时，我们的图的平整度也会发生变化。我们还研究了时间延迟对所提出的植物病害动力学的作用，以及感染率对易感人群和感染人群的影响。这项研究的主要动机是考察记忆效应下分数导数意义上的病媒传染病动力学。本研究是分式导数在植物流行病学中的应用实例。等维度卡普托导数的应用包括模型中的记忆，这是本研究的主要创新之处。

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引用次数: 0

The inhomogeneous p-Laplacian equation with Neumann boundary conditions in the limit p→∞documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} 极限p中具有Neumann边界条件的非齐次p-拉普拉斯方程→∞documentclass[12pt]｛minimal｝ usepackage｛amsmath｝ use package｛｛wasysym｝usepackage{amsfonts} usepackage{amssymb｝ userpackage{amsbsy｝usepackage｛mathrsfs｝ user package{upgeek｝setlength｛doddsidemargin｝｛-69pt｝

Q1 MATHEMATICS

Advances in continuous and discrete models

Pub Date : 2021-12-14 DOI: 10.1186/s13662-023-03754-8

Leon Bungert

引用次数: 1

A second-order low-regularity integrator for the nonlinear Schrödinger equation 非线性Schrödinger方程的二阶低正则积分器

Q1 MATHEMATICS

Advances in continuous and discrete models

Pub Date : 2021-09-02 DOI: 10.1186/s13662-022-03695-8

A. Ostermann, Yifei Wu, Fangyan Yao

引用次数: 8

Path classification by stochastic linear recurrent neural networks 随机线性递归神经网络的路径分类

Q1 MATHEMATICS

Advances in continuous and discrete models

Pub Date : 2021-08-06 DOI: 10.1186/s13662-022-03686-9

Y. Boutaib, Wiebke Bartolomaeus, Sandra Nestler, H. Rauhut

引用次数: 1

Operator compression with deep neural networks 算子压缩与深度神经网络

Q1 MATHEMATICS

Advances in continuous and discrete models

Pub Date : 2021-05-25 DOI: 10.1186/s13662-022-03702-y

Fabian Kröpfl, R. Maier, D. Peterseim

引用次数: 9

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