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21st IFAC World Congress on Automatic Control - Meeting Societal Challenges

作者： Ruediger, Jens Tech Univ Appl Sci Wildau Hsch Ring 1 D-15745 Wildau Germany

A reliable energy supply for the economy of every country is a matter of national importance. Powerful simulation tools for natural gas networks are essential for operators of gas networks. In this paper, enhancement algorithms of previous developed node potential analysis algorithm are presented. These enhancement algorithms are used for a reasonable setting of initial values in the numerical gas net simulation algorithm. The setting of the initial values has a significant influence on the convergence behavior of the numerical simulation. The presented enhancement algorithms are explained and simulation results are evaluated. Copyright (C) 2020 The Authors.

关键词： energy supply gas net pipelines natural gas simulation numerical algorithm

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Enhancements of the numerical simulation algorithm for natural gas networks based on node potential analysis

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IFAC-PapersOnLine 2020年第2期53卷 13119-13124页

作者： Jens Rüdiger Technical University of Applied Sciences Wildau Hochschulring 1 15745 Wildau Germany

关键词： energy supply gas net pipelines natural gas simulation numerical algorithm

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numerical Solution of Second-Order Impulsive Differential Equations With Loadings Subject to Integral Boundary Conditions

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MATHEMATICAL METHODS IN THE APPLIED SCIENCES 2025年第6期48卷 6269-6277页

作者： Kadirbayeva, Zhazira Kadirbayeva, Roza Inst Math & Math Modeling Alma Ata Kazakhstan Kazakh Natl Womens Teacher Training Univ Alma Ata Kazakhstan Int Informat Technol Univ Alma Ata Kazakhstan South Kazakhstan Pedag Univ Shymkent Kazakhstan

In this paper, we present a computational method for solving the second-order impulsive differential equations with loadings subject to integral boundary conditions based on the Dzhumabaev parametrization method. The idea of this method involves introducing additional parameters, reducing the original problem to solving a system of linear algebraic equations. The system's coefficients and right-hand side are determined by solving Cauchy problems for ODEs and by calculating definite integrals. Four examples are provided to show the effectiveness and feasibility of the main results.

关键词： impulsive differential equations integral conditions loadings numerical algorithm parametrization method

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Entropy optimization and Prandtl-Eyring non-Newtonian fluid flow with second-order slip conditions past a curved Riga sheet;numerical simulation

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INTERNATIONAL JOURNAL OF THERMAL SCIENCES 2025年 214卷

作者： Ali, Bilal Zhou, Yue-Ting Jubair, Sidra Tariq, Muzammal Hameed Kumar, Abhinav Siddiqui, Md Irfanul Haque Tongji Univ Sch Aerosp Engn & Appl Mech Shanghai 200092 Peoples R China Shanghai Inst Aircraft Mech & Control 100 Zhangwu Rd Shanghai 200092 Peoples R China Dalian Univ Technol Sch Math Sci Dalian 116024 Peoples R China Ural Fed Univ Dept Nucl & Renewable Energy Ekaterinburg 620002 Russia Karpagam Acad Higher Educ Dept Mech Engn Coimbatore 641021 India Western Caspian Univ Dept Tech Sci Baku Azerbaijan King Saud Univ Coll Engn Dept Mech Engn Riyadh 12372 Saudi Arabia

The non-Newtonian (NN) Prandtl-Eyring fluid (PEF) model can be used to optimize conditions for processing, ensure substance high quality and consistency, and anticipate melted polymer flow behavior. This paper looks into an intriguing feature of irreversibility estimation through NN-PEF flow over a curved Riga surface. The impact of second-order slip conditions, thermal radiation, and exponential heat source/sink are also elaborated. The flow equations of NN-PEF have been reformulated into a dimensionless representation of differential equations (DEs) with an application of similarity conversions. The obtained lowest-order differential equations are numerically solved through the PCM (parametric continuation method). For accuracy of the results, the outcomes are compared to both experimental and theoretical results. The relative percent error between the present findings and the published numerical results at Re = 5000 is 0.71094 %. The rate of heat transfer (W/ m2K) enhances from 4238.0724 to 44390.4205 at Re = 1594 to 440. The relative error between published experimental and present results is about 0.0029 % at Re = 440, which ensures the reliability of the proposed model and applied methodology. The velocity field of PEF is significantly boosted with the positive variation in 1st and 2nd order slip parameters. The influence of the Brinkmann number and heat radiation factor is enhanced, while the consequences of the temperature ratio parameter drop the rate of entropy generation in the system.

关键词： Entropy optimization Experimental validation Second-order slip conditions Non-Newtonian Prandtl-Eyring fluid numerical algorithm Curved Riga sheet

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High accuracy analysis of three-dimensional axisymmetric nonlinear boundary integral equations☆

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ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS 2025年 176卷

作者： Li, Hu Huang, Jin Chengdu Normal Univ Sch Math Chengdu 611130 Peoples R China Univ Elect Sci & Technol China Sch Math Sci Chengdu 611731 Peoples R China

In this paper, we consider the numerical solutions of three-dimensional axisymmetric nonlinear boundary integral equations with logarithmic kernel. A numerical algorithm with using extrapolation twice is developed to solve the equations, which possesses the low computing complexities and high accuracy. The asymptotic compact operator theory is used to prove the convergence of the algorithm. The efficiency of the algorithm is illustrated by numerical examples.

关键词： numerical algorithm Quadratic extrapolation Axisymmetric nonlinear boundary integral equations

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numerical algorithms for image geometric transformations and applications

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IEEE TRANSACTIONS ON SYSTEMS MAN AND CYBERNETICS PART B-CYBERNETICS 2004年第1期34卷 132-149页

作者： Li, ZC Wang, FQ Liao, SSY Natl Sun Yat Sen Univ Dept Appl Math Kaohsiung 804 Taiwan City Univ Hong Kong Dept Informat Syst Kowloon Hong Kong Peoples R China

To facilitate images under the nonlinear geometric transformation T and its inverse transformation T-1, we have developed numerical algorithms in [1]-[19]. A cycle conversion T-1T of image transformations is said if an image is distorted by a transformation T and then restored back to itself. The combination (CSIM) of splitting-shooting-integrating methods was first proposed in Li [1] for T-1T. In this paper other two combinations, CUM and C&IM, of splitting integrating methods for T-1T are provided. Combination CSIM has been successfully applied to many topics in image processing and pattern recognition (see [2]). Since combination CSIM causes large greyness errors, it well suited to a few greyness level images, but needs a huge computation work for 256 greyness level images of enlarged transformations (see [16]). We may instead choose combination CIIM which involves nonlinear solutions. However, the improved combination CI#IM may bypass the nonlinear solutions completely. Hence, both CIIM and CI#IM can be applied to q(q greater than or equal to 256) greyness level images of arty enlarged transformations. On the other hand, the combined algorithms, CSIM, CIIM, and CI#IM, are applied to several important topics of image processing and pattern recognition: binary images, multi-greyness level images, image condensing, illumination, affine transformations, prospective and projection, wrapping images, handwriting characters, image concealment, the transformations with arbitrary shapes, and face transformation. This paper may also be regarded as a review of our recent research papers [1]-[19].

关键词： blending model computer version digital images and patterns harmonic model image geometric transformation numerical algorithm pattern recognition splitting-integration method splitting-shooting method

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numerical algorithmS FOR BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS WITH 1-D BROWNIAN MOTION: CONVERGENCE AND SIMULATIONS

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ESAIM-MATHEMATICAL MODELLING AND numerical ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE 2011年第2期45卷 335-360页

作者： Peng, Shige Xu, Mingyu Shandong Univ Sch Math & Syst Sci Jinan 250100 Peoples R China Chinese Acad Sci Acad Math & Syst Sci Key Lab Random Complex Struct & Data Sci Beijing Peoples R China Fudan Univ Sch Math Sci Dept Financial Math & Control Sci Shanghai 200433 Peoples R China

In this paper we study different algorithms for backward stochastic differential equations (BSDE in short) basing on random walk framework for 1-dimensional Brownian motion. Implicit and explicit schemes for both BSDE and reflected BSDE are introduced. Then we prove the convergence of different algorithms and present simulation results for different types of BSDEs.

关键词： Backward stochastic differential equations reflected stochastic differential equations with one barrier numerical algorithm numerical simulation

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Game Theory and Dual Approach to the Dynamic Programming on the Example of the COVID-19 Pandemic in Poland Described by Mathematical Model With Three-Dose Vaccinated

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OPTIMAL CONTROL APPLICATIONS & METHODS 2025年第2期46卷 647-664页

作者： Matusik, Radoslaw Univ Lodz Fac Math & Comp Sci Lodz Poland

In this paper, a new approach to the disease transmission dynamics of the COVID-19 pandemic is presented, involving the use of game theory and dual dynamic programming. A new compartmental model that describes these dynamics is introduced. New classes have been added to this model to account for the portion of the population vaccinated with one dose, two doses, or three doses. Pandemic costs are also included. Time-dependent parameters (strategies) are employed, allowing for the consideration of different behavior variants and decisions made by policymakers. Sufficient conditions for a dual epsilon-closed-loop Nash equilibrium, are formulated in the form of a verification theorem. A numerical algorithm is constructed, and numerical simulations are performed. A comparison between real pandemic data for Poland and the data obtained from the model is made.

关键词： COVID-19 dual epsilon-closed-loop Nash equilibrium dual dynamic programming game model of the pandemic numerical algorithm

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Fast convergence of the primal-dual dynamical system and corresponding algorithms for a nonsmooth bilinearly coupled saddle point problem

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2025年第1期90卷 151-192页

作者： Ding, Ke-wei Fliege, Jorg Vuong, Phan Tu Southwest Minzu Univ Sch Math Chengdu 610041 Sichuan Peoples R China Univ Southampton Math Sci Southampton SO17 1BJ England

This paper studies the convergence rate of a second-order dynamical system associated with a nonsmooth bilinearly coupled convex-concave saddle point problem, as well as the convergence rate of its corresponding discretizations. We derive the convergence rate of the primal-dual gap for the second-order dynamical system with asymptotically vanishing damping term. Based on an implicit discretization scheme, we propose a primal-dual algorithm and provide a non-ergodic convergence rate under a general setting for the inertial parameters when one objective function is continuously differentiable and convex and the other is a proper, convex and lower semicontinuous function. For this algorithm we derive a O1/k2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O\left( 1/k<^>2 \right) $$\end{document} convergence rate under three classical rules proposed by Nesterov, Chambolle-Dossal and Attouch-Cabot without assuming strong convexity, which is compatible with the results of the continuous-time dynamic system. For the case when both objective functions are continuously differentiable and convex, we further present a primal-dual algorithm based on an explicit discretization. We provide a corresponding non-ergodic convergence rate for this algorithm and show that the sequence of iterates generated weakly converges to a primal-dual optimal solution. Finally, we present numerical experiments that indicate the superior numerical performance of both algorithms.

关键词： Saddle point problem Primal-dual dynamical system Convergence rate numerical algorithm Nesterov's accelerated gradient method Iterates convergence

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The Split Quaternion Least Squares Problem With Equality Constraint and Its Application

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MATHEMATICAL METHODS IN THE APPLIED SCIENCES 2025年

作者： Zhou, Zhi-Han Meng, Zi-Xiang Li, Ying Zhang, Feng-Xia Liaocheng Univ Coll Math & Sci Liaocheng Peoples R China

By applying the real representation matrix and the Moore-Penrose inverse of the split quaternion matrix, we first study the split quaternion least squares problem with equality constraint (SQLSE) and obtain its general solution and minimum norm solution. Then, we obtain the Karush-Kuhn-Tucker equation, which is an equivalent problem of the SQLSE problem. Immediately after, we propose a numerical algorithm on the real number field for the minimum norm solution of the SQLSE problem and enumerate three examples to display its validity. Eventually, we provide an application of the SQLSE problem in the color image restoration.

关键词： color image restoration equality constraint numerical algorithm real representation matrix split quaternion least squares problem

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