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(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)

program codes for communication

实现FastICA功能，非线性函数分别选取高斯函数，三次函数和正切函数。(Realize FastICA function, non-linear function were selected gaussian function, three function and tangent function.)

Calculate the NPCR between images

基于循环前缀的符号定时同步和载波同步的ofdm仿真的matlab程序(Symbol Timing and Carrier Synchronization of ofdm Matlab simulation procedures.)

he fi eld of plasmonics has grown dramatically over the past decade, and still continues growing towards new directions enabling new fundamental science and device tech-nologies. Research in this area explores how electromagnetic fi elds can be confi ned over dimensions smaller than the wavelength. It is based on interaction processes between elec-tromagnetic radiation and conduction electrons at metallic interfaces or in small metallic nanostructures.(he fi eld of plasmonics has grown dramatically over the past decade, and still continues growing towards new directions enabling new fundamental science and device tech-nologies. Research in this area explores how electromagnetic fi elds can be confi ned over dimensions smaller than the wavelength. It is based on interaction processes between elec-tromagnetic radiation and conduction electrons at metallic interfaces or in small metallic nanostructures.)

结合物理光学、几何光学原理，通过matlab对光学中基本的光学现象进行了模拟(Physical optics, geometrical optics principle matlab optics basic optical phenomena are simulated)

四足液压机器人设计程序，界面化例程，包括四足机器人正逆运动学，动力学，轨迹规划，驱动元件的设计与选用等，对四足机器人的设计开发具有指导。(Quadruped hydraulic robot design program, the interface routines, including a quadruped robot kinematics and inverse kinematics, dynamics, trajectory planning, drive components of the design and selection, of quadruped robot design and development with guidance.)

物理光学上的干涉实验，用matlab编程来实现，比较实用！(Intervention on physical optics experiments with matlab programming to achieve more practical!)

用MATLAB实现遗传算法的程序，可以无限制的套用，仅供参考！(it is good!)