chebfun 包的安装与使用

chebfun 包的安装与使用

最近在学习如何使用chebfun包，以防自己忘记随手记录博客

Matlab安装

官方文档可见链接：
Guide
下载后并解压，在当前文件夹下，在命令行窗口输入

movefile('chebfun-master', 'chebfun'), addpath(fullfile(cd,'chebfun')), savepath

下面运行一个demo测试是否安装成功

x = chebfun('x');
f = sin(12*x).*exp(-x);         % A function on [-1, 1]
g = max(f, 1./(x+2));           % The max of f and 1./(x+2)
plot(g)                         % A function with discontinuous derivative
sum(g)                          % The integral of g
plot(diff(g))                   % The derivative of g
h = g + x - .8;                 % A function with several roots in [-1, 1]
rr = roots(h);                  % Compute the roots of h
plot(h, 'k', rr, h(rr), 'ro')   % Plot h and its roots

可得结果

ans =

    1.4619

及图片

MATLAB中利用Chebfun求解PDE实例

mathworks关于Chebfun包的详解链接: chebfun_mathworks

UU = PDE15s(PDEFUN, TT, U0, BC) where PDEFUN is a handle to a function with
    arguments u, t, x, and D, TT is a vector, U0 is a CHEBMATRIX, and BC is a
    chebop boundary condition structure will solve the PDE dUdt = PDEFUN(UU, t,
    x) with the initial condition U0 and boundary conditions BC over the time
    interval TT.

例1 Kuramoto-Sivashinsky 方程

一个非线性偏微分方程

      x = chebfun('x');
      u = 1 + 0.5*exp(-40*x.^2);
      bc.left = @(u) [u - 1 ; diff(u)];
      bc.right = @(u) [u - 1 ; diff(u)];
      f = @(u) u.*diff(u) - diff(u, 2) - 0.006*diff(u, 4);
      opts = pdeset('Ylim', [-30 30], 'PlotStyle', {'LineWidth', 2});
      uu = pde15s(f, 0:.01:.5, u, bc, opts);
      surf(uu, 0:.01:.5)

例 2 Nonuniform advection方程

      x = chebfun('x', [-1 1]);
      u = exp(3*sin(pi*x));
      f = @(t, x, u) -(1 + 0.6*sin(pi*x)).*diff(u) + 5e-5*diff(u, 2);
      opts = pdeset('Ylim', [0 20], 'PlotStyle', {'LineWidth', 2});
      uu = pde23t(f, 0:.05:3, u, 'periodic', opts);
      surf(uu, 0:.05:3)

例3 Chemical reaction (system)

x = chebfun('x');
       u = [ 1 - erf(10*(x+0.7)) ; 1 + erf(10*(x-0.7)) ; 0 ];
       f = @(u, v, w)  [ .1*diff(u, 2) - 100*u.*v ; ...
                         .2*diff(v, 2) - 100*u.*v ; ...
                         .001*diff(w, 2) + 2*100*u.*v ];
       opts = pdeset('Ylim', [0 2], 'PlotStyle', {'LineWidth', 2});
       [t, u, v, w] = pde15s(f, 0:.1:3, u, 'neumann', opts);
       mesh(uu{3})

Python安装

安装命令

pip install pychebfun