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非线性约束优化问题的新方法——微分方程逼近
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作者 周宗放 《大自然探索》 1999年第4期78-79,共2页
1 引言自1958年Arrow,Hurwicz和Uzawa提出用微分方程处理无约束优化问题后,Branin和Hoo在70年代前后也相继提出处理无约束优化问题的斜量曲线方程和Newton型曲线方程。与此同时,Botsaris和J... 1 引言自1958年Arrow,Hurwicz和Uzawa提出用微分方程处理无约束优化问题后,Branin和Hoo在70年代前后也相继提出处理无约束优化问题的斜量曲线方程和Newton型曲线方程。与此同时,Botsaris和Jacobson(1970),Vail(197... 展开更多
关键词 非线性 约束优化问题 微分方程逼近 ODE法
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Adomian Decomposition Method and Padé Approximants for Nonlinear Differential-Difference Equations 被引量:1
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作者 LIU Yan-Ming CHEN Yong 《Communications in Theoretical Physics》 SCIE CAS CSCD 2009年第4期581-587,共7页
Combining Adomian decomposition method (ADM) with Pade approximants, we solve two differentiaidifference equations (DDEs): the relativistic Toda lattice equation and the modified Volterra lattice equation. With t... Combining Adomian decomposition method (ADM) with Pade approximants, we solve two differentiaidifference equations (DDEs): the relativistic Toda lattice equation and the modified Volterra lattice equation. With the help of symbolic computation Maple, the results obtained by ADM-Pade technique are compared with those obtained by using ADM alone. The numerical results demonstrate that ADM-Pade technique give the approximate solution with faster convergence rate and higher accuracy and relative in larger domain of convergence than using ADM. 展开更多
关键词 Adomian decomposition method Pade approximants relativistic Toda lattice equation modified Volterra lattice equation
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Solitary Solution of Discrete mKdV Equation by Homotopy Analysis Method 被引量:1
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作者 WANG Zhen ZOU Li ZHANG Hong-Qing 《Communications in Theoretical Physics》 SCIE CAS CSCD 2008年第6期1373-1378,共6页
In this paper, we apply homotopy analysis method to solve discrete mKdV equation and successfully obtain the bell-shaped solitary solution to mKdV equation. Comparison between our solution and the exact solution shows... In this paper, we apply homotopy analysis method to solve discrete mKdV equation and successfully obtain the bell-shaped solitary solution to mKdV equation. Comparison between our solution and the exact solution shows that homotopy analysis method is effective and validity in solving hybrid nonlinear problems, including solitary solution of difference-differential equation. 展开更多
关键词 differential-difference equation Homotopy analysis method homotopy-Pade approximation discrete mKdV equation SOLITON
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Statistical Average of Spin Operators for Calculation of Three-Component Magnetization
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作者 WANGHuai-Yu ZHOUBin CHENNan-Xian 《Communications in Theoretical Physics》 SCIE CAS CSCD 2005年第4期753-758,共6页
When one wants to calculate all the three components of magnetization of Heisenberg model under random phase approximation, at least one of the components should be the solution of an ordinary differential equation. I... When one wants to calculate all the three components of magnetization of Heisenberg model under random phase approximation, at least one of the components should be the solution of an ordinary differential equation. In this paper such an equation is established. It is argued that the general expressions of magnetization for any spin quantum number S suggested before are the solution of the ordinary differential equation. 展开更多
关键词 three-component magnetization heisenberg model many-body Green's functionmethod ordinary differential equation
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Exact Travelling Solutions of Discrete sine-Gordon Equation via Extended Tanh-Function Approach
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作者 DAI Chao-Qing ZHANG Jie-Fang 《Communications in Theoretical Physics》 SCIE CAS CSCD 2006年第1X期23-27,共5页
In this paper, we generalize the extended tanh-function approach, which was used to find new exact travelling wave solutions of nonlinear partial differential equations or coupled nonlinear partial differential equati... In this paper, we generalize the extended tanh-function approach, which was used to find new exact travelling wave solutions of nonlinear partial differential equations or coupled nonlinear partial differential equations, to nonlinear differential-difference equations. As illustration, two series of exact travelling wave solutions of the discrete sine-Gordon equation are obtained by means of the extended tanh-function approach. 展开更多
关键词 discrete sine-Gordon equation exact travelling wave solution extended tanh-function approach
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Localized collocation schemes and their applications 被引量:1
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作者 Zhuojia Fu Zhuochao Tang +3 位作者 Qiang Xi Qingguo Liu Yan Gu Fajie Wang 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2022年第7期1-28,I0002,共29页
This paper presents a summary of various localized collocation schemes and their engineering applications.The basic concepts of localized collocation methods(LCMs)are first introduced,such as approximation theory,semi... This paper presents a summary of various localized collocation schemes and their engineering applications.The basic concepts of localized collocation methods(LCMs)are first introduced,such as approximation theory,semianalytical collocation methods and localization strategies.Based on these basic concepts,five different formulations of localized collocation methods are introduced,including the localized radial basis function collocation method(LRBFCM)and the generalized finite difference method(GFDM),the localized method of fundamental solutions(LMFS),the localized radial Trefftz collocation method(LRTCM),and the localized collocation Trefftz method(LCTM).Then,several additional schemes,such as the generalized reciprocity method,Laplace and Fourier transformations,and Krylov deferred correction,are introduced to enable the application of the LCM to large-scale engineering and scientific computing for solving inhomogeneous,nonisotropic and time-dependent partial differential equations.Several typical benchmark examples are presented to show the recent developments and applications on the LCM solution of some selected boundary value problems,such as numerical wave flume,potential-based inverse electrocardiography,wave propagation analysis and 2D phononic crystals,elasticity and in-plane crack problems,heat conduction problems in heterogeneous material and nonlinear time-dependent Burgers’equations.Finally,some conclusions and outlooks of the LCMs are summarized. 展开更多
关键词 Localization Collocation method Semianalytical Computational mechanics
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A branching particle system approximation for nonlinear stochastic filtering 被引量:1
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作者 LIU HuiLi XIONG Jie 《Science China Mathematics》 SCIE 2013年第8期1521-1541,共21页
The optimal filter 7r = {π,t ∈ [0, T]} of a stochastic signal is approximated by a sequence {Try} of measure-valued processes defined by branching particle systems in a random environment (given by the observation ... The optimal filter 7r = {π,t ∈ [0, T]} of a stochastic signal is approximated by a sequence {Try} of measure-valued processes defined by branching particle systems in a random environment (given by the observation process). The location and weight of each particle are governed by stochastic differential equations driven by the observation process, which is common for all particles, as well as by an individual Brownian motion, which applies to this specific particle only. The branching mechanism of each particle depends on the observation process and the path of this particle itself during its short lifetime δ = n-2α, where n is the number of initial particles and ~ is a fixed parameter to be optimized. As n → ∞, we prove the convergence of π to πt uniformly for t ∈ [0, T]. Compared with the available results in the literature, the main contribution of this article is that the approximation is free of any stochastic integral which makes the numerical implementation readily available. 展开更多
关键词 optimal filter branching particle system uniform convergence numerical solution
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