Results in Applied Mathematics最新文献_第9页

Uncovering a generalised gamma distribution: From shape to interpretation 揭示广义伽马分布：从形状到解释

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Results in Applied Mathematics Pub Date : 2024-05-01 DOI: 10.1016/j.rinam.2024.100461

Matthias Wagener , Andriette Bekker , Mohammad Arashi , Antonio Punzo

引用次数: 0

Inverting the sum of two singular matrices 反转两个奇异矩阵之和

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Results in Applied Mathematics Pub Date : 2024-05-01 DOI: 10.1016/j.rinam.2024.100463

Sofia Eriksson, Jonas Nordqvist

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A reciprocal integral identity of coupled Poisson and Laplace equations in two arbitrary domains sharing a common boundary 共享共同边界的两个任意域中耦合泊松方程和拉普拉斯方程的互积分特性

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Results in Applied Mathematics Pub Date : 2024-05-01 DOI: 10.1016/j.rinam.2024.100464

Sai Sashankh Rao, Harris Wong

{"title":"A reciprocal integral identity of coupled Poisson and Laplace equations in two arbitrary domains sharing a common boundary","authors":"Sai Sashankh Rao, Harris Wong","doi":"10.1016/j.rinam.2024.100464","DOIUrl":"https://doi.org/10.1016/j.rinam.2024.100464","url":null,"abstract":"<div><p>In solving the coupled vapor and liquid unidirectional flows in micro heat pipes, we discovered numerically an integral identity. After asymptotic and polynomial expansions, the coupled flows yield two reciprocal systems of equations. In system A, a vapor velocity <span><math><msub><mi>U</mi><mi>A</mi></msub></math></span> obeys the Poisson equation and drives, through an interfacial boundary condition, a liquid velocity <span><math><msub><mi>W</mi><mi>A</mi></msub></math></span> that satisfies the Laplace equation. In reciprocal system B, a liquid velocity <span><math><msub><mi>W</mi><mi>B</mi></msub></math></span> obeys the Poisson equation and drives, through another interfacial boundary condition, a vapor velocity <span><math><msub><mi>U</mi><mi>B</mi></msub></math></span> that satisfies the Laplace equation. We found that the vapor volume flow rate of <span><math><msub><mi>U</mi><mi>B</mi></msub></math></span> is numerically equal to the liquid volume flow rate of <span><math><msub><mi>W</mi><mi>A</mi></msub></math></span> for seven different pipe shapes. Here, a general proof is presented for the integral identity, and some interesting implications of this identity are discussed.</p></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"22 ","pages":"Article 100464"},"PeriodicalIF":2.0,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2590037424000347/pdfft?md5=15ef6456818b39be2398537f95248bf5&pid=1-s2.0-S2590037424000347-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141242564","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

TDOR-MPINNs: Multi-output physics-informed neural networks based on time differential order reduction for solving coupled Klein–Gordon–Zakharov systems TDOR-MPINNs：基于时差阶减的多输出物理信息神经网络，用于求解耦合克莱因-戈登-扎哈罗夫系统

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Results in Applied Mathematics Pub Date : 2024-05-01 DOI: 10.1016/j.rinam.2024.100462

Jiahuan He, Yang Liu, Hong Li

{"title":"TDOR-MPINNs: Multi-output physics-informed neural networks based on time differential order reduction for solving coupled Klein–Gordon–Zakharov systems","authors":"Jiahuan He, Yang Liu, Hong Li","doi":"10.1016/j.rinam.2024.100462","DOIUrl":"https://doi.org/10.1016/j.rinam.2024.100462","url":null,"abstract":"<div><p>With the continuous development in the field of deep learning, in recent years, it has also been widely used in the field of solving partial differential equations, especially the physics-informed neural networks (PINNs) method. However, the PINNs method has some limitations in solving coupled Klein–Gordon–Zakharov (KGZ) systems. To this end, in this article, inspired by the PINNs method and combined with the characteristics of the coupled KGZ systems, we design a neural network model, named multi-output physics-informed neural networks based on time differential order reduction (TDOR-MPINNs), to solve the coupled KGZ systems. Compared with the PINNs, the TDOR-MPINNs first reduces the time derivatives, and thus can increase supervised learning tasks. And through comparing the numerical results obtained by using TDOR-MPINNs and PINNs for solving the one-dimensional (1-D) and two-dimensional (2-D) coupled KGZ systems, we further validate the effectiveness, accuracy and reliability of the TDOR-MPINNs.</p></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"22 ","pages":"Article 100462"},"PeriodicalIF":2.0,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2590037424000323/pdfft?md5=a2129c10b3b5d8d2bd0e79f34b38b6d5&pid=1-s2.0-S2590037424000323-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140918743","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

Positivity-preserving discontinuous Galerkin scheme for linear hyperbolic equations with characteristics-informed augmentation 线性双曲方程的保正性非连续伽勒金方案与特征信息增量

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Results in Applied Mathematics Pub Date : 2024-05-01 DOI: 10.1016/j.rinam.2024.100460

Maurice S. Fabien

{"title":"Positivity-preserving discontinuous Galerkin scheme for linear hyperbolic equations with characteristics-informed augmentation","authors":"Maurice S. Fabien","doi":"10.1016/j.rinam.2024.100460","DOIUrl":"https://doi.org/10.1016/j.rinam.2024.100460","url":null,"abstract":"<div><p>This paper presents a positivity-preserving discontinuous Galerkin (DG) scheme for the linear hyperbolic problem with variable coefficients on structured Cartesian domains. The standard DG spaces are augmented with either polynomial or non-polynomial basis functions. The primary purpose of these augmented basis functions is to ensure that the cell average from the unmodulated DG scheme remains positive. We explicitly obtain suitable basis functions by inspecting the method of characteristics on an auxiliary problem. A key result is proved which demonstrates that the unmodulated augmented DG scheme will retain a positive cell average, provided that the inflow, source term, and variable coefficients are positive. A simple scaling limiter can then be leveraged to produce a high-order conservative positivity-preserving DG scheme. Numerical experiments demonstrate the scheme is able to retain high-order accuracy as well as robustness for variable coefficients. To improve efficiency, an inexact augmented basis function can be obtained rather than a analytic non-polynomial solution to the auxiliary problem from the method of characteristics.</p></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"22 ","pages":"Article 100460"},"PeriodicalIF":2.0,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S259003742400030X/pdfft?md5=5573fad70bfa36dcb674d85f812a20a9&pid=1-s2.0-S259003742400030X-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140879869","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

Numerical solutions of sea turtle population dynamics model by using restarting strategy of PINN-Adam 利用 PINN-Adam 重启策略数值求解海龟种群动态模型

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Results in Applied Mathematics Pub Date : 2024-04-25 DOI: 10.1016/j.rinam.2024.100457

Danang A. Pratama , Maharani A. Bakar , Ummu Atiqah Mohd Roslan , Sugiyarto Surono , A. Salhi

引用次数: 0

Numerical solution of singularly perturbed singular third order boundary value problems with nonclassical sinc method 用非经典 sinc 法数值求解奇异扰动奇异三阶边界值问题

IF 2

Results in Applied Mathematics Pub Date : 2024-04-22 DOI: 10.1016/j.rinam.2024.100459

A. Alipanah, K. Mohammadi, R.M. Haji

引用次数: 0

A hybrid-based numerical method for a class of systems of mixed Volterra–Fredholm integral equations 一类 Volterra-Fredholm 混合积分方程系统的混合数值方法

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Results in Applied Mathematics Pub Date : 2024-04-17 DOI: 10.1016/j.rinam.2024.100458

F. Afiatdoust , M.M. Hosseini , M.H. Heydari , M. Mohseni Moghadam

引用次数: 0

Finite element error estimation for parabolic optimal control with measurement data 利用测量数据对抛物线优化控制进行有限元误差估计

IF 2

Results in Applied Mathematics Pub Date : 2024-04-16 DOI: 10.1016/j.rinam.2024.100456

Xun Yang, Xianbing Luo

引用次数: 0

A class of new implicit compact sixth-order approximations for Poisson equations and the estimates of normal derivatives in multi-dimensions 一类新的泊松方程隐式紧凑六阶近似和多维度正态导数估计

IF 2

Results in Applied Mathematics Pub Date : 2024-04-15 DOI: 10.1016/j.rinam.2024.100454

R.K. Mohanty , Niranjan

{"title":"A class of new implicit compact sixth-order approximations for Poisson equations and the estimates of normal derivatives in multi-dimensions","authors":"R.K. Mohanty , Niranjan","doi":"10.1016/j.rinam.2024.100454","DOIUrl":"https://doi.org/10.1016/j.rinam.2024.100454","url":null,"abstract":"<div><p>In this piece of work, a family of compact implicit numerical algorithms for (<em>∂u/∂n</em>) of order of accuracy six are proposed on a 9- and 19-point compact cell for two- and three- dimensional Poisson equations <em>∆</em><sup>2</sup><em>u</em>=<em>f</em> which are quite often useful in mathematical physics and engineering, where <em>∆</em><sup>2</sup> is either two or three dimensional Laplacian operator. First, we propose a family of new numerical algorithms of order of accuracy six for the computation of the solution of 2D and 3D Poisson equations on 9- and 27-points compact stencil, respectively. Then with the aid of the numerical solution of <em>u</em>, we propose a new family of compact sixth order implicit numerical algorithms for the estimates of (<em>∂u/∂n</em>). The proposed algorithms are free from derivatives of the source functions, which makes our algorithms more efficient for computation. Suitable iteration techniques are used for computation to demonstrate the sixth order convergence of the proposed algorithms. Numerical results are tabulated, confirming the usefulness of the suggested numerical algorithms.</p></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"22 ","pages":"Article 100454"},"PeriodicalIF":2.0,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2590037424000244/pdfft?md5=777275bd087413d156989f36e77a860d&pid=1-s2.0-S2590037424000244-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140555015","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