PID-algrithm

递归神经网络-实时学习训练算法代码，亲测可用，简洁无误，容易上手。( Recursive neural network- real-time learning training algorithm code, pro-test available, simple and correct, easy to use.)

数值模拟方腔内Rayleigh-Benard对流。采用交错网格投影法，能量方程采用松耦合方法。(Numerical Simulation of square cavity Rayleigh-Benard convection. Using staggered grid projection method, the energy equation using loosely coupled approach.)

本程序是用MGS正交化方法求方程组的最小二乘解的程序(This program is the program of MGS orthogonalization method and the least squares solution of equations)

fluent 旋转边界算例，可以了解运动机械在fluent模拟中的设置(fluent rotation the boundary example, you can understand the mechanical movement set in fluent simulation)

对离散点进行多项式拟合，不同于传统多项式拟合高次出现病态，此程序可以拟合高阶多项式( ORTHOFIT Fit polynomial to data. YS = ORTHOFIT(X,Y,N) smooths/fits data Y(X) in a least-squares sense using a polynomial of degree N and returns the smoothed data YS.)

说明：  实现快速离散傅里叶变换，即FFT,很有用的程序(Fast discrete Fourier transform, namely, FFT, very useful program)

一个表达式计算库，支持算术，逻辑运算，位运算，支持多层级的if/then/else，功能强大。(Calculation of an expression library, support for arithmetic, logic operations, bit computing, multi-level support if/then/else, powerful.)

说明：  四级四阶龙格库塔格式，求解微分方程的好算法。(Four fourth-order Runge-Kutta format, a good algorithm for solving differential equations.)

粒子群算法在解决非线性方程上的应用，给出了详细程序(Particle swarm algorithm for solving nonlinear equations, gives detailed procedures)

说明：  二维河道水动力模型；matlab 迭代程序；水质模拟(Two dimensional river hydrodynamic model; MATLAB iterative program; water quality simulation)