prime

(有源代码)数值分析作业,本文主要包括两个部分,第一部分是常微分方程(ODE)的三个实验题,第二部分是有关的拓展讨论,包括高阶常微分的求解和边值问题的求解(BVP).文中的算法和算例都是基于Matlab计算的.ODE问题从刚性(STIFFNESS)来看分为非刚性的问题和刚性的问题,刚性问题(如大系数的VDP方程)用通常的方法如ODE45来求解,效率会很低,用ODE15S等,则效率会高多了.而通常的非刚性问题,用ODE45来求解会有很好的效果.从阶次来看可以分为高阶微分方程和一阶常微分方程,高阶的微分方程一般可以化为状态空间(STATE SPACE)的低阶微分方程来求解.从微分方程的性态看来,主要是微分方程式一阶导系数大的时候,步长应该选得响应的小些.或者如果问题的性态不是太好估计的话,用较小的步长是比较好的,此外的话Adams多步法在小步长的时候效率比R-K(RUNGE-KUTTA)方法要好些,而精度也高些,但是稳定区间要小些.从初值和边值来看,也是显著的不同的.此外对于非线性常微分方程还有打靶法,胞映射方法等.而对于微分方程稳定性的研究,则诸如相平面图等也是不可缺少的工具.值得提出的是,除了用ode系类函数外,用simulink等等模块图来求解微分方程也是一种非常不错的方法,甚至是更有优势的方法(在应用的角度来说).((Source code) numerical analysis homework, this docment includes two parts, the first is ordinary differential equations (ODE) of the three examples, the second part is about the expansion of the discussion, including the higher-order ordinary differential & boundary value solution Problems (BVP). the text of the algorithm and numerical examples are based on the Matlab. ODE from the rigid (STIFFNESS) look into the issue of non-rigid and rigid problem, rigid problems (such as large coefficient VDP equation) such as using the always method ODE45 used to solve the problems , efficiency will be low, with ODE15S the other hand, many of the high efficiency. and the usual problem of non-rigid, there will be used to solve ODE45 very good results. Judging from the order can be for high-order differential equations and first-order ordinary differential equations, higher-order differential equations can be transformed into a general state space (STATE SPACE) used to solve the low-order different)

电源-地同步噪声电磁仿真程序，用FDTD编写的，可以参考一下，终端匹配(applies finite difference time domain method to analyze transmission coefficient.)

第二代curvelet变换工具箱，有快速傅里叶变换和wraping变换方法，还可以提取变换系数。有matlab版本和c++版本(The second generation of curvelet transform toolbox, with fast Fourier transform and wraping transform method, also can extract transform coefficient.With the matlab version and c++ version)

利用matlab编写的fdtd模拟程序！(Fdtd using matlab simulation program written!)

This code is one application of visible watermarking.

14节点的无功优化是用粒子群算法实现的，很实用，希望对大家有帮助。(14-node reactive power optimization is achieved using particle swarm algorithm, very practical, we hope to help.)

pso解决两目标函数极值问题，适合初学多目标的同学(Pso solve two goals for beginners, the function extreme problem multi-objective classmates)

steepest descent method for estimation

声音信号的处理以及重新编译，其中包含完整的code以及lab report(UNDERSTAND SIMULATION SOFTWARE OF MATLAB TO PLOT SIGNALS)

关于信号处理方面音效移频中解析信号的产生方法，该方法让人耳目一新，通过先设计频域，再求逆，时域上进行采样，得到两个FIR滤波器逼近希尔伯特变换器。(Aboat an efficient method of analytical signal generation in audio frequency shift.This method refreshing, first design in the frequency domain, then sampling in the time domain, getting two FIR filters approximate Hilbert transform.)