在线时间:8:00-16:00
迪恩网络APP
随时随地掌握行业动态
扫描二维码
关注迪恩网络微信公众号
Kuiken 利用相似变换,得到如下非线性微分方程 满足如下边界条件 其中, 表示对 求导,为普朗特数. 此方程是耦合的非线性边值问题,在无穷远点具有奇性.
当 时,使用Matlab的bvp4c求解如下: 将原方程转化为一阶方程组 % kuikenode.m function df=kuikenode(eta,f) sigma=1; df=[ f(2) f(3) f(2)^2-f(4) f(5) 3*sigma*f(2)*f(4)]; 输入边界条件 % kuikenbc.m function res=kuikenbc(f0,finf) res =[f0(1) f0(2) f0(4)-1 finf(2) finf(4)]; 以常数作为初始猜测解 % kuikeninit.m function v=kuikeninit(eta) v =[ 0 0 1 0 0]; 调用bvp4c求解,注意此处无界区间被截断 % solve.m clc; clear; infinity=30; solinit=bvpinit(linspace(0,infinity,5),@kuikeninit); options=bvpset('stats','on','RelTol', 1e-12); sol=bvp4c(@kuikenode,@kuikenbc,solinit,options); eta=sol.x; g=sol.y; fprintf('\n'); fprintf('Kuiken reports f''''(0) = 0.693212.\n') fprintf('Value computed here is f''''(0) = %7.7f.\n',g(3,1)) fprintf('Kuiken reports %c''(0) = -0.769861.\n', char([952])) fprintf('Value computed here is %c''(0) = %7.7f.\n',char([952]),g(5,1)) clf reset subplot(1,2,1); plot(eta,g(2,:)); axis([0 infinity 0 1]); title('Kuiken equation, \sigma =1.') xlabel('\eta') ylabel('df/d\eta') subplot(1,2,2); plot(eta,g(4,:)); axis([0 infinity 0 1]); title('Kuiken equation, \sigma = 1.') xlabel('\eta') ylabel('\theta') shg 运行如下:
The solution was obtained on a mesh of 105 points. |
2023-10-27
2022-08-15
2022-08-17
2022-09-23
2022-08-13
请发表评论