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2025 International Conference on Electrical Automation and Artificial Intelligence, ICEAAI 2025

作者： Yang, Wentao Jin, Aochen Sun, Hao Yang, Wenbin Guangxi University College of Electrical Engineering Nanning China China Mobile Industry Research Institute The R&D Department II Chengdu China

ISBN: (纸本)9798331506797

The time scale span of energy transmission in the electric gas thermal integrated energy system is enormous, and the mathematical modeling of dynamic processes in multi-energy flow systems at different time scales is very complex. The simulation efficiency and accuracy of multi-energy flow systems are difficult to balance, and the accurate characterization of system response faces great challenges. In response to the above issues, this paper proposes a multi-time scale simulation method of integrated energy systems based on finite difference approximation. Firstly, the partial differential equations of gas and heat pipelines are discretized using the finite difference approximation theory, and a dynamic model involving time delay in gas and heat pipelines is established. Secondly, according to the breadth-first traversal algorithm, network constraints are met to connect coupled devices and networks. Finally, the simulation of the real operating state of the system when encountering small disturbances or faults verifies that the dynamic model proposed in this paper can significantly reduce the complexity and computational volume of the model, and improve simulation efficiency while ensuring accuracy. © 2025 IEEE.

关键词： dynamic characteristic analysis finite difference approximation Integrated energy system multi-time scale transmission delay

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finite difference approximation FOR PRICING THE AMERICAN LOOKBACK OPTION

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Journal of Computational Mathematics 2009年第4期27卷 484-494页

作者： Tie Zhang Shuhua Zhang Danmei Zhu Department of Mathematics School of Information Science and Engineering Northeastern University Shenyang 110003 China Research Center for Mathematics and Economies Tianjin University of Finance and Economics Tianjin 300222 China Department of Mathematics School of Information Science and Engineering Northeastern University Shenyang 110004 China

In this paper we are concerned with the pricing of lookback options with American type constrains. Based on the differential linear complementary formula associated with the pricing problem, an implicit difference scheme is constructed and analyzed. We show that there exists a unique difference solution which is unconditionally stable. Using the notion of viscosity solutions, we also prove that the finite difference solution converges uniformly to the viscosity solution of the continuous problem. Furthermore, by means of the variational inequality analysis method, the O（△t ＋ △x^2）-order error estimate is derived in the discrete L2-norm provided that the continuous problem is sufficiently regular. In addition, a numerical example is provided to illustrate the theoretical results.

关键词： American lookback options finite difference approximation Stability andconvergence Error estimates.

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A TOXIN-MEDIATED SIZE-STRUCTURED POPULATION MODEL: finite difference approximation AND WELL-POSEDNESS

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MATHEMATICAL BIOSCIENCES AND ENGINEERING 2016年第4期13卷 697-722页

作者： Huang, Qihua Wang, Hao Univ Alberta Dept Math & Stat Sci Edmonton AB T6G 2G1 Canada

The question of the effects of environmental toxins on ecological communities is of great interest from both environmental and conservational points of view. Mathematical models have been applied increasingly to predict the effects of toxins on a variety of ecological processes. Motivated by the fact that individuals with different sizes may have different sensitivities to toxins, we develop a toxin-mediated size-structured model which is given by a system of first order fully nonlinear partial differential equations (PDEs). It is very possible that this work represents the first derivation of a PDE model in the area of ecotoxicology. To solve the model, an explicit finite difference approximation to this PDE system is developed. Existence-uniqueness of the weak solution to the model is established and convergence of the finite difference approximation to this unique solution is proved. Numerical examples are provided by numerically solving the PDE model using the finite difference scheme.

关键词： Size-structured model toxin finite difference approximation existence-uniqueness

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A finite difference approximation for Dynamic Calculation of Vertical Free Hanging Slender Risers in Re-Entry Application

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China Ocean Engineering 2012年第4期26卷 637-652页

作者：王盛炜徐雪松姚宝恒连琏 School of Naval Architecture Ocean and Civil EngineeringShanghai Jiao Tong University

The dynamic calculations of slender marine risers, such as finite Element Method （FEM） or Modal Expansion Solution Method （MESM）, are mainly for the slender structures with their both ends hinged to the surface and bottom. However, for the re-entry operation, risers held by vessels are in vertical free hanging state, so the displacement and velocity of lower joint would not be zero. For the model of free hanging flexible marine risers, the paper proposed a finite difference approximation （FDA） method for its dynamic calculation. The riser is divided into a reasonable number of rigid discrete segments. And the dynamic model is established based on simple Euler-Bemoulli Beam Theory concerning tension, shear forces and bending moments at each node along the cylindrical structures, which is extendible for different boundary conditions. The governing equations with specific boundary conditions for riser＇s free hanging state are simplified by Keller-box method and solved with Newton iteration algorithm for a stable dynamic solution. The calculation starts when the riser is vertical and still in calm water, and its behavior is obtained along time responding to the lateral forward motion at the top. The dynamic behavior in response to the lateral parametric excitation at the top is also proposed and discussed in this paper.

关键词： finite difference approximation free hanging slender risers Keller-box method Newton iteration re-entryapplication

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Implicit finite difference approximation for time fractional diffusion equations

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2008年第4期56卷 1138-1145页

作者： Murio, Diego A. Univ Cincinnati Dept Math Sci Cincinnati OH 45221 USA

Time fractional diffusion equations are used when attempting to describe transport processes with long memory where the rate of diffusion is inconsistent with the classical Brownian motion model. In this paper we develop an implicit unconditionally stable numerical method to solve the one-dimensional linear time fractional diffusion equation, formulated with Caputo's fractional derivative, on a finite slab. Several numerical examples of interest are also included. (C) 2008 Elsevier Ltd. All rights reserved.

关键词： finite difference approximation implicit method time fractional diffusion fractional differentiation unconditional stability

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On the consistency of the finite difference approximation with the Riemann-Liouville fractional derivative for 0 <α <1

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APPLIED NUMERICAL MATHEMATICS 2020年 153卷 35-51页

作者： Duan, Hui Chen, Xinjuan Jung, Jae-Hun Florida State Univ Dept Math Tallahassee FL 32306 USA Ajou Univ Dept AI & Data Sci Suwon 16499 South Korea SUNY Buffalo Dept Math Buffalo NY 14260 USA

Fractional differential equations have become an important modeling technique in describing various natural phenomena. A variety of numerical methods for solving fractional differential equations has been developed over the last decades. Among them, finite difference methods are most popular owing to relative easiness for implementation. In this paper, we show that the finite difference method with the Riemann-Liouville (RL) fractional derivative yields inconsistent and oscillatory numerical solutions to fractional differential equations of discontinuous problems for the fractional order alpha, 0 < alpha < 1. Such an inconsistency affects even smooth problems since the numerical solution can be regarded as a discontinuous function over grids. We show that the inconsistency inherited in discontinuous problems causes the numerical solution for smooth problems to be oscillatory under certain conditions although the magnitude of the oscillations decreases as the number of grids, N, increases. That is, although the truncation error is decaying as N -> infinity and the method is consistent for smooth problems, the numerical solution can be oscillatory for any value of N. To illustrate the inconsistency and the oscillation phenomenon with the RL method, we also consider the finite difference methods with the Caputo and Grunwald-Letnikov fractional derivatives and compare the results with by with the RL method. We also show that the integral approach for the RL method can resolve the issues of the inconsistency and the oscillation phenomenon. Numerical results are presented to support the statements. (C) 2020 IMACS. Published by Elsevier B.V. All rights reserved.

关键词： Fractional derivatives Riemann-Liouville derivative Grunwald-Letnikov derivative Caputo derivative finite difference approximation Discontinuous problems

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Indirect solution of optimal control problems with state variable inequality constraints: finite difference approximation

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ROBOTICA 2017年第1期35卷 50-72页

作者： Nikoobin, A. Moradi, M. Semnan Univ Fac Mech Engn Semnan Iran Semnan Univ Fac Elect & Comp Engn Semnan Iran

In this paper, a method for the indirect solution of the optimal control problem (OCP) in the presence of pure state variable inequality constraints (SVICs) and mixed state-control inequality constraints (SCIC), without a need for a close initial guess is presented. In the proposed method, using the finite difference approximation (FDA), the pure SVICs are converted to SCIC. Here, the distance of the constraint function to the feasibility bounds of the constraint is computed in every situation and the control signal is chosen appropriately to facilitate the constraint stays safe. In this method, prior knowledge of the numbers and sequences of activation times is not required. So, it can be simply implemented in continuous boundary value problem (BVP) solvers. The proposed method simply applies the SVICs and since the constraint is directly applied on the control signal, it improves the convergence. On the other hand, because of the convergence problem in the indirect solution of OCP, the simple homotopy continuation method (HCM) is used to overcome the initial guess problem by deploying a secondary OCP for which the initial guess can be zero. The proposed approach is applied on a few comprehensive problems in the presence of different constraints. Simulations are compared with the direct solution of the OCP to confirm the accuracy and with the penalty function method and the sequential constraint-free OCP to confirm the convergence. The results indicate that the FDA method for handling the constraints along with the HCM is easy to apply with acceptable accuracy and convergence, even for highly nonlinear problems in robotic systems such as the constrained time optimal control of a two-link manipulator (TLM) and a three-link common industrial robot.

关键词： Optimal control Indirect solution Pontryagin maximum principle State variable inequality constraint Homotopy method finite difference approximation

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Numerical solution of 2D Navier-Stokes equation discretized via boundary elements method and finite difference approximation

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ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS 2018年 96卷 64-77页

作者： Sedaghatjoo, Zeynab Dehghan, Mehdi Hosseinzadeh, Hossein Amirkabir Univ Technol Fac Math & Comp Sci Dept Appl Math 424 Hafez Ave Tehran Iran Persian Gulf Univ Dept Math Bushehr Iran

In this paper boundary elements method (BEM) is equipped with finite difference approximation (FDA) to solve two-dimensional Navier-Stokes (N-S) equation. The N-S equation is converted to a system of ordinary differential equations (ODEs) respect to time in streamfunction-vorticity formulation. The constant direct BEM and 9-point stencil FDA are utilized to handle spatial derivatives, and the final system of ODEs is solved via three numerical schemes, forward Euler, Runge-Kutta and Newton's methods to find a fast ODE solver. Numerical investigations presented in this article show Newton's method is faster than the others and it is able to solve the N-S equation for Reynolds number up to 40,000 when grid points are at most 141 x 141. Thanks to BEM and boundary conditions of lid-driven cavity flow, the final system of ODEs is stable also for higher Reynolds numbers. A new technique is proposed in this article which converts BEM's two-dimensional singular integrals to one-dimensional non-singular ones. The proposed technique reduces computational cost of BEM, significantly, when more accurate results are requested. Numerical experiments show the numerical results are fairly agree with that accurate ones available in the literature.

关键词： Boundary elements method finite difference approximation Navier-Stokes equation Ordinary differential equations and system of ODEs Streamfunction-vorticity formulation High Reynolds number Runge-Kutta formula and Newton's method

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Propagation of One- and Two-Dimensional Discrete Waves Under finite difference approximation

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FOUNDATIONS OF COMPUTATIONAL MATHEMATICS 2020年第6期20卷 1401-1438页

作者： Biccari, Umberto Marica, Aurora Zuazua, Enrique Friedrich Alexander Univ Erlangen Nurnberg Dept Math D-91058 Erlangen Germany Fdn Deusto Chair Computat Math Avda Univ 24 Bilbao 48007 Basque Country Spain Univ Deusto Fac Ingn Avda Univ 24 Bilbao 48007 Basque Country Spain Univ Politehn Bucuresti Dept Math & Comp Sci Fac Sci Appl Splaiul Independentei 313 Bucharest 060042 Romania Univ Bucharest Univ Bucharest ICUB Res Inst Bucharest Romania Univ Autonoma Madrid Dept Matemat E-28049 Madrid Spain

We analyze the propagation properties of the numerical versions of one- and two-dimensional wave equations, semi-discretized in space by finite difference schemes. We focus on high-frequency solutions whose propagation can be described, both at the continuous and at the semi-discrete levels, by micro-local tools. We consider uniform and non-uniform numerical grids as well as constant and variable coefficients. The energy of continuous and semi-discrete high-frequency solutions propagates along bi-characteristic rays, but their dynamics are different in the continuous and the semi-discrete setting, because of the nature of the corresponding Hamiltonians. One of the main objectives of this paper is to illustrate through accurate numerical simulations that, in agreement with micro-local theory, numerical high-frequency solutions can bend in an unexpected manner, as a result of the accumulation of the local effects introduced by the heterogeneity of the numerical grid. These effects are enhanced in the multi-dimensional case where the interaction and combination of such behaviors in the various space directions may produce, for instance, the rodeo effect, i.e., waves that are trapped by the numerical grid in closed loops, without ever getting to the exterior boundary. Our analysis allows to explain all such pathological behaviors. Moreover, the discussion in this paper also contributes to the existing theory about the necessity of filtering high-frequency numerical components when dealing with control and inversion problems for waves, which is based very much on the theory of rays and, in particular, on the fact that they can be observed when reaching the exterior boundary of the domain, a key property that can be lost through numerical discretization.

关键词： Wave equation finite difference approximation Uniform and non-uniform meshes Propagation of solutions

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A finite difference approximation for a coupled system of nonlinear size-structured populations

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NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 2002年第6期50卷 727-748页

作者： Ackleh, AS Banks, HT Deng, K Univ Louisiana Lafayette Dept Math Lafayette LA 70504 USA N Carolina State Univ Ctr Res Sci Computat Raleigh NC 27695 USA

An initial boundary value problem describing the dynamics of coupled size-structured subpopulations with nonlinear growth, reproduction and mortality rates was considered. The population was treated as being composed of several populations with different growth rates. The inverse problem of identifying the growth rate distribution was solved. It was shown that the generalized models differed crucially from the classical Sinko-Streifer models and dispersion of population density in age or size are absent in the classical models.

关键词： coupled system of size-structured populations existence-uniqueness finite difference approximation competition extinction survival

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