用同伦摄动法求一类非线性问题的近似解

利用同伦摄动法可得出一类非线性方程的近似解.部分特殊方程的求解得到详细分析.     

Burgers-Huxley方程的同伦分析解

针对Burgers-Huxley方程定解问题,构造了一种零阶同伦方程,采用同伦方法得到Burgers-Huxley方程定解问题的近似解析解.最后,进行了实例验证和结果分析.     

非线性互补问题的凝聚同伦方法

给出凝聚函数的性质,利用凝聚函数构造同伦方程,证明了同伦路径的存在性,有界性和收敛性,给出非单调函数拟P_*-映射满足严格可行条件时所对应的互补问题的可解性.     

求解特征值反问题的同伦方法

§1.引言 本文讨论经典的加法问题,即 问题A.给定一个n阶实对称矩阵A和n个实数λ_1,…,λ_n,求n维实向量x=(x_,…,x_n)~T,使得A+diag(x_1,…,x_n)的特征值是λ_1,…,λ_n。 求解问题A的数值方法已有很多,一般是先把问题A化为一个等价的非线性方程组,然后用Newton法求解相应的非线性方程组.在[6]中,Friedland等对这方面的工     

Duffing简谐振子同伦分析法求解

利用同伦分析方法求解了Duffing简谐振子,数值确定了变形方程中的辅助参数,得到了一族响应和频率的近似周期解,该解与精确解符合很好,结果表明,同伦分析法在求解强非线性振子时,仍然是一种行之有效的方法.     

大范围求解非线性方程组的指数同伦法

为了解决关于奇异的非线性方程组求根问题,提出了一种由同伦算法推出大范围收敛的连续型方法-指数同伦法,构造了一类指数同伦方程,克服了Jacobi矩阵的奇异,分析了指数同伦方     

一类窄带随机激励下的非线性问题的同伦解法

利用同伦映射理论,研究了一类窄带随机激励下的非线性问题,在适当的条件下,较简捷地得到了问题解较高精度的估计式.     

求解一类非线性规划的连续同伦方法(英文)

In this paper we present a homotopy continuation method for finding the Karush-Kuhn-Tucker point of a class of nonlinear non-convex programming problems. Two numerical examples are given to show that this method is effective. It should be pointed out that we extend the results of Lin et al. （see Appl. Math. Comput., 80（1996）, 209-224） to a broader class of non-convex programming problems.     

同伦分析法求解Burgers方程的初边值问题

采用同伦分析法求解了Burgers方程的一初边值问题,得到了它的近似解析解.在不同粘性系数情形下,对近似解与精确解进行了比较,发现在粘性系数不是非常小的情况下,用此方法得到的解析解与精确解符合地很好.     

A New Homotopy Method for Nonlinear Complementarity Problems

In this paper, we present a new homotopy method for the nonlinear complementarity problems. Without the regularity or non-singulary assumptions for▽F(x), we prove that our homotopy equations have a bounded solution curve. The numerical tests confirm the efficiency of our proposed method.     

非线性互补问题的组合同伦算法

针对拟P_*-映射和P(τ,α,β)-映射所对应的非线性互补问题,本文对其解的存在性及有效求解算法进行了研究.文中利用组合同伦方法给出了这两类非线性互补问题存在有界解的构造性证明,并利用预估校正方法对同伦路径进行跟踪,得到了互补问题的解.通过数值算例验证了该算法的有效性.     

Nonlinear Frequency Analysis of FGM Pipes Based on the Homotopy Method北大核心CSCD

Based on the homotopy analysis method, the nonlinear vibration of porous functionally graded material (FGM) conveying pipes under generalized boundary conditions was studied. Based on the power-law distribution of the FGM and the Voigt model, the physical properties of the porous pipe material were described. Under the Euler-Bernoulli beam theory and the von Kármán nonlinear theory, and by means of Hamilton’s variational principle, the dynamic control equations and generalized boundary conditions for porous FGM conveying pipes were established. The homotopy analysis method was used to solve the nonlinear vibration characteristics of the porous FGM conveying pipe under generalized boundary conditions. The numerical results show that, the translation spring has little effect on the critical velocity of instability, while the rotation spring increases the critical velocity of instability, making the system more stable; in the nonlinear system, the viscoelastic coefficient does not change the critical velocity; the pipe length, the power-law exponent and the porosity all influence the nonlinear free vibration of the porous FGM conveying pipe. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

一类海-气振子ENSO模型的同伦分析解法

研究了一个ENSO海-气时滞振子模型.利用同伦分析方法,得到了该模型解的近似展开式,通过与特殊情况下的精确解比较,得到的二级近似解具有较高的精度.     

A Combined Homotopy Infeasible Interior-Point Method for Convex Nonlinear Programming

In this paper, on the basis of the logarithmic barrier function and KKT conditions , we propose a combined homotopy infeasible interior-point method (CHIIP) for convex nonlinear programming problems. For any convex nonlinear programming, without strict convexity for the logarithmic barrier function, we get different solutions of the convex programming in different cases by CHIIP method.     

基于同伦分析方法的一种改进的试位法

应用同伦分析方法,提出了一种求解非线性方程改进的试位法．给出的一些数值例证显示了该运算法则的有效性．     

求解线性互补问题的同伦方法

It is well known that a linear complementarity problem (LCP) can be formulated as a system of nonsmooth equations F(x) = 0, where F is a map from Rninto itself. Using the aggregate function, we construct a smooth Newton homotopy H(x,t) = 0. Under certain assumptions, we prove the existence of a smooth path defined by the Newton homotopy which leads to a solution of the original problem, and study limiting properties of the homotopy path.     

求解非线性方程的一种线化和校正方法

提出了一种拟摄动理论——线化和校正方法。在该理论中,不象传统的摄动方法假设其近似解可表示成小参数的级数形式,而是先把方程线性化,再求其线化方程的解,然后再校正线化方程的解。这样得到的近似解不受方程中的“参数”的影响。