利用模糊Laplace变换的方法求解模糊分数阶积分微分方程

研究了模糊非线性Caputo意义下分数阶积分微分方程。通过应用改进的模糊Laplace变换和Adomian分解方法,找到了一个非线性模糊分数阶积分微分方程的近似解,最后给出例子进行说明。     

关于三阶发展方程初边值问题的解

本文应用 Adomian 分解法有效的求出了三阶发展方程带初边值问题的解。     

利用改进的Adomian分解法求解Lotka-Volterra捕食模型

Lotka-Volterra捕食模型是一类重要的非线性系统.利用改进的Adomian分解法求解捕食模型,得到了方程的高阶解析近似解并进行了误差分析.结果表明,改进后的Adomian分解法精度更高,更能有效地描述生物链中种群捕食关系.     

逆算符理论方法在求解一维相对论振子振动方程中的应用

本文应用逆算符理论方法－Adomian分解求解一维相对论振子的振动方程,得到10阶逼近解,并将此解与文献[1]作比较。     

广义Black-Scholes方程的算子级数解

本文主要研究系数依赖时间和空间的非齐次的广义Black-Scholes方程,结合一些引理和推论,将Adomian分解法推广到求解更一般的广义Black-Scholes方程的数值解。利用Adomian分解法,我们得到广义Black-Scholes方程的含有算子形式迭代的一般级数解,同时证明该方法对广义Black-Scholes方程同样适用。     

用Adomian分解法求带有分数阶导数的加热一般第二级流体的Stokes第一类问题

考虑一般第二级流体的Stokes第一类问题.为了描述这样一个流体,在基本关系模型里引进分数阶微积分学方法.但是,有效地求解分数阶加热一般第二级流体的Stokes第一类问题(简写为SFP-HGSGF)的方法仍然不多.在此利用Adomian分解方法构造近似解.最后用一些数值例子来说明此方法的有效性、可靠性和简单性.     

一类非线性分数阶微分方程解的边值问题

文中运用Adomian方法研究了Banach空间中一类非线性分数阶微分方程的边值问题,主要通过krasnosel'skill不动点定理和Banach压缩映射原理给出该问题存在的充分条件,最后推广已有的某些结果。     

一类Volterra捕食者-食饵模型的解析解

文中介绍了Adomian分解法,并用这种方法来求一类Volterra模型的定量行为,同时讨论了解的有关性质.研究工作表明,该方法具有相当广泛的适应性.     

基于改进Adomian分解法的分数阶Rabinovich超混沌系统实验仿真北大核心

采用改进Adomian分解法对分数阶Rabinovich超混沌系统进行仿真。从系统单参数变化下的分岔图、复杂度C0数值仿真分析了分数阶Rabinovich超混沌系统从周期到混沌所具有的动力学行为,运用双参数变化下的复杂度研究了系统分岔空间的特点。仿真结果表明:分数阶混沌系统阶数q越大,系统复杂度越低。这种理论与仿真相结合的方法使得学生能深入理解了分数阶动力学系统,有效地提高了教学质量。     

逆算符理论方法在求解一维相对论振子振动方程中的应用

应用逆算符理论方法－－Ａｄｏｍｉａｎ分解法求解一维相对论振子的振动方程得到１０阶逼近解。     

Decomposition method for solving parabolic equations in finite domains

INTRODUCTION The decomposition method was introduced by Adomian(1989;1994)in the1980’s for solving linear and nonlinear functional equations(algebraic,dif-ferential,partial differential equations(PDEs)and systems,integral,differential-delay,integro-differen-tial equations,etc.)(Adomian,1989;1994;Guellal and Cherruault,1995;Adomian et al.,1996;Laffez and Abbaoui,1996;Ndour et al.,1996;Guellal et al.,1997;Abbaoui and Cherruault,1999;Adjedj,1999).This method leads to computable,accurat…     

改进的变分迭代法在Fokker-Planck方程中的应用

讨论将改进的变分迭代法应用于Fokker-Planck方程或者其相似的方程并求精确解.通过其简便的计算得到方程的解,与Adomian分裂法对比可知变分迭代法求收敛解的速度比后者要快速、简单.     

基于Masson区间映射误差理论的方盒模型研究

Masson的最小误差模型理论提出了一种新的方盒模型,对该模型的一些性质进行了研究;用模糊数学中分解定理的思想完成了模型的模糊化,使之可以处理模糊数据;然后利用Masson区间多维标度法思想,将非线性映像扩展到区间非线性映像和模糊集非线性映像。     

Control synthesis for polynomial nonlinear systems and application in attitude control

A method for positive polynomial validation based on polynomial decomposition is proposed to deal with control synthesis problems. Detailed algorithms for decomposition are given which mainly consider how to convert coefficients of a polynomial to a matrix with free variables. Then, the positivity of a polynomial is checked by the decomposed matrix with semidefinite programming solvers. A nonlinear control law is presented for single input polynomial systems based on the Lyapunov stability theorem. The control synthesis method is advanced to multi-input systems further. An application in attitude control is finally presented. The proposed control law achieves effective performance as illustrated by the numerical example.     

一类分数阶偏微分方程的正则性分析

讨论了一类分数阶对流-扩散方程,首先用分离变量法求出方程的解,然后用Adomian拆分法通过数值算例与分离变量法的结果进行比较,验证了方法的有效性.接着讨论了方程的强解、正则性、连续性等性质.     

A hybrid EMD-AR model for nonlinear and non-stationary wave forecasting

Accurate wave forecasting with a couple of hours of warning time offers improvements in safety for maritime operation-related activities. Autoregressive (AR) model is an efficient and highly adaptive approach for wave forecasting. However, it is based on linear and stationary theory and hence has limitations in forecasting nonlinear and non-stationary waves. Inspired by the capability of empirical mode decomposition (EMD) technique in handling nonlinear and non-stationary signals, this paper describes the development of a hybrid EMD-AR model for nonlinear and non-stationary wave forecasting. The EMDAR model was developed by coupling an AR model with the EMD technique. Nonlinearity and non-stationarity were overcome by decomposing the wave time series into several simple components for which the AR model is suitable. The EMD-AR model was implemented using measured significant wave height data from the National Data Buoy Center, USA. Prediction results from various locations consistently show that the hybrid EMD-AR model is superior to the AR model. This demonstrates that the EMD technique is effective in processing nonlinear and non-stationary waves.     

Matrix decomposition and Lagrangian dual method for discrete portfolio optimization under concave transaction costs

In this paper, the discrete mean-variance model is considered for portfolio selection under concave transaction costs. By using the Cholesky decomposition technique, the convariance matrix to obtain a separable mixed integer nonlinear optimization problem is decomposed. A brand-and-bound algorithm based on Lagrangian relaxation is then proposed. Com-putational results are reported for test problems with the data randomly generated and those from the US stock market.     

Measurement of moment of inertia based on hilbert transform

A measurement model based on torsion pendulum was established,in which nonlinear damping and nonlinear restoring force were considered.The calculation method of the moment of inertia was based on Hilbert transform.The motion of torsion pendulum showed the time-frequency characteristics due to the nonlinear factors,which were validated by the experimental data.The analytical signal was formed by Hilbert transform of the angular displacement signal of the test object.The moment of inertia can be computed by the instantaneous undamped natural frequency with Hilbert transform.Prior to the implementation of Hilbert transform,the empirical mode decomposition was used to filter the experimental signal.The moment of inertia of the test object was measured by the torsion pendulum system.The experimental results show that the relative measurement error of the moment of inertia was within 0.7%,which indicated the validity of the measurement method.     

一类非线性项含有所有阶导数的梁方程的可解性

利用Schauder不动点定理研究了一类非线性四阶边值问题的解和正解的存在性。主要工具是方程的分解技巧和二阶两点边值问题的Green函数。在力学中，这类问题描述了一端简单支撑，另一端滑动的弹性梁的形变。