{matrix} 1+2r& -r& 0& 0& \cdots& 0\\ -r& 1+2r& -r& 0& \cdots& 0\\ 0& -r& 1+2r& -r& \cdots& 0\\ \vdots& \vdots& \vdots& \vdots& \vdots& \vdots\\ 0& \cdots& \cdots& -r& 1+2r& -r\\ 0& \cdots& \cdots& 0& -r& 1+2r\\ \end{matrix}...
在前面的基础上: 迦非喵:C++Tridiagonal matrix algorithm 简单测试迦非喵:国产CFD开源软件OneFLOW求解一维热传导方程简单测试(Crank–Nicolson scheme version2)这里继续重构: 有: CMakeList.txt cmake_mi…
此格式是一个隐式格式，需要求解一个线性方程组来获得下一时间层的解。这个方程组可以用追赶法（Tri-diagonal Matrix Algorithm）解决，复杂度为O(N)，其中N为网格点总数。Crank-Nicolson差分格式精度较高，对于时间步长Δt和空间步长Δx,Δy的选择有一定的限制，一般而言，Δt应该小于Δx²/(4D)。
Crank-Nicolson Implicit Scheme Tridiagonal Matrix Solver via Thomas Algorithm In theprevious tutorialon Finite Difference Methods it was shown that the explicit method of numerically solving the heat equation lead to an extremely restrictive time step. This motivates another scheme which allows for larger...
Using the matrix representation for the numerical scheme and boundary conditions it is shown that for implicit boundary conditions the Crank–Nicolson scheme is unrestrictedly stable while it becomes conditionally stable for explicit boundary conditions. Numerical examples are provided illustrating this ...
However, in this work it was realized that, when the time step is set above CFL limit the coefficient matrix arising from Crank-Nicolson method is no longer diagonally dominant and iterative solvers require longer solution time in each FDTD iteration. Frequency dependent CN-FDTD (FD-CN-FDTD) ...
CrankNicolson method 1 Crank –Nicolson method In numerical analysis, the Crank –Nicolson method is a finite difference method used for numerically solving the heat equation and similar partial differential equations.[1] It is a second-order method in time, implicit in time, and is numerically ...
修正局部Crank-Nicolson法对变系数扩散方程的应用 通过将所研究的偏微分方程转化为常微分方程组,利用指数函数的Trotter积公式近似该常微分方程组的系数矩阵并分离成分块小矩阵,再利用Crank-Nicolson法求得结果,推出变... 黄鹏展,阿布都热西提.阿布都外力 - 《吉林大学学报(理学版)》 被引量: 16发表: 2008年 非定常...
The updated version of the Crank–Nicolson smoothing procedure for barrier options is then given as follows:(10)un+1=R0,1(kA)un,tn∈Sp,R1,1(kA)un,else.We thus re-apply the damping strategy p times (usually p=2, 3 or 4) at each barrier. Since we have a fixed number of barriers...
在前面的基础上: 迦非喵:国产CFD开源软件OneFLOW加入Tridiagonal matrix algorithm简单测试1 赞同 · 0 评论文章 迦非喵:国产CFD开源软件OneFLOW求解一维热传导方程简单测试(third-order Runge-Kutta version3)1 赞同 · 0 评论文章 这里继续重构: 参考: