LU

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.)

一个实现sor超松弛迭代法的c语言算法，可以帮助新手完成矩阵计算(A C language algorithm for realizing over relaxation iterative method)

自己写了一个二维Euler方程的间断有限元程序 上次发了一个三角形单元的程序 因为不是曲边单元 所以在圆柱后面容易形成涡 现在把程序改为曲边四边形单元了 没有涡出现 单元是8节点四边形单元 节点编号顺序是 1 5 2 6 3 7 4 8 也就是四个角点依次 是1 2 3 4 然后是边的中点编号 5 6 7 8. 时间推进采用 Runge-Kutta 方法 数值通量采用全局Lax-Friedrichs通量 仍然不能捕捉激波 因为没有做重构或者加人工粘性 等这个做出来了 再发一次。 程序没有进行优化 比如说内存的消耗没有优化 比如直边单元的边界积分仍然采 用了曲边的积分方法 增加了计算量 比如面积分、线积分都是采用的是Gauss- Legendre-Lobatto积分 积分精度会比一般的Gauss-Legendre积分精度低一阶 等 等问题。 二维的 纯属交流性质 就没有考虑这些问题 ^_^ 如果物面全部是直边 那么只要改变一个参数N 就可以获得不同的计算精度 且具 有谱精度 因为单元的节点是Gauss-Legendre-Lobatto积分点。 其实就是谱元法 （物面是曲边的情况我不清楚是不是也可以通过提高基函数的阶数 也就是增加N 来提高计算精度）(Wrote a two-dimensional Euler equations with discontinuous finite element program Last made ​ ​ a triangular element of the program, not curved edge unit is so easy to form a vortex in the cylinder behind the Program to curved edge quadrilateral element vortices appear Unit is the order of 8-node quadrilateral element node number is 15,263,748 which is the four corners of the points in turn Is 1234 and then the side of the midpoint of the number 5678. Time promote the use of Runge-Kutta method Numerical flux of the overall situation of Lax-Friedrichs, flux Still can not capture the shock wave did not do the reconstruction or artificial viscosity do it Zaifayici. The program is not optimized for example, memory consumption is not optimized such as straight-edge boundary integral of the unit is still mining Integral method to increase the amount of computation such as surface integral with a curved edge, the line integral using the Gauss- The Legendr)

艾特金迭代法求解线性方程组源代码，在程序中修改方程就可以(Aitkin iterative method for solving linear equations source code, the equation can be modified in the program)

传输矩阵法用于计算光纤光栅的有效折射率，是一种经典的数学算法(Matrix function)

说明：  研究舍入误差的例程，可以帮助初学计算方法的人。(Of rounding error in the routine that can help beginners who calculation.)

c++的有限元源码,带说明书和测试数据,是难得的有限元开发资料.(This is the code of finite element method, with manual document and data samples, it is valusble for FEM development)

最优潮流计算程序（使用电力系统专业，属于非线性规划问题）．(optimal power flow calculation procedure (using power systems professional, is Nonlinear Programming).)

运用物理光学法和矩量法计算带罩天线的远场辐射(The use of physical optics method and moment method with cover antenna far-field radiation )

吉尔算法积分一阶微分方程组初值问题的C语言描述，包括主函数、计算微分方程组中各方程右端函数值的函数程序、计算雅克比矩阵的函数程序、矩阵求逆程序等。(GEAR algorithm integral first order differential equations initial value problem of the C language description, including the main function to calculate the differential equations in the equation right function value function procedures, functions Jacobian matrix calculation procedures, matrix inversion procedures.)