MATLAB解偏微分方程

think2015

1. <div style="text-align: center;"><img src="http://forum.vibunion.com/forum.php?mod=image&aid=71816&size=300x300&key=a007c670780730af&nocache=yes&type=fixnone" border="0" aid="attachimg_71816" alt=""></div><div><span style="font-size: 14px; line-height: 1.5;">
   
2. </span></div><div><span style="font-size: 14px; line-height: 1.5;">function </span><wbr style="font-size: 14px; line-height: 1.5;"><span style="font-size: 14px; line-height: 1.5;"> </span><wbr style="font-size: 14px; line-height: 1.5;"><span style="font-size: 14px; line-height: 1.5;"> </span><wbr style="font-size: 14px; line-height: 1.5;"><span style="font-size: 14px; line-height: 1.5;"> </span><wbr style="font-size: 14px; line-height: 1.5;"><span style="font-size: 14px; line-height: 1.5;">zzz</span></div><div>
   
3. <span style="word-wrap: normal; word-break: normal;">% <wbr> <wbr>主函数：</span>
   
4. <span style="word-wrap: normal; word-break: normal;">x=0:0.05:1;</span>
   
5. <span style="word-wrap: normal; word-break: normal;">t=0:0.05:2;</span>
   
6. <span style="word-wrap: normal; word-break: normal;">m=0;</span>
   
7. <span style="word-wrap: normal; word-break: normal;">sol=pdepe(m,@pdefun,@pdeic,@pdebc,x,t);</span>
   
8. <span style="word-wrap: normal; word-break: normal;">figure('numbertitle','off','name','PDE <wbr>Demo')</span>
   
9. <span style="word-wrap: normal; word-break: normal;">subplot(211)</span>
   
10. <span style="word-wrap: normal; word-break: normal;">surf(x,t,sol(:,:,1))</span>
    
11. <span style="word-wrap: normal; word-break: normal;">title('The <wbr>solution <wbr>of <wbr>u_1')</span>
    
12. <span style="word-wrap: normal; word-break: normal;">xlabel('X')</span>
    
13. <span style="word-wrap: normal; word-break: normal;">ylabel('T')</span>
    
14. <span style="word-wrap: normal; word-break: normal;">zlabel('U')</span>
    
15. <span style="word-wrap: normal; word-break: normal;">subplot(212)</span>
    
16. <span style="word-wrap: normal; word-break: normal;">surf(x,t,sol(:,:,2))</span>
    
17. <span style="word-wrap: normal; word-break: normal;">title('The <wbr>Solution <wbr>of <wbr>u_2')</span>
    
18. <span style="word-wrap: normal; word-break: normal;">xlabel('X')</span>
    
19. <span style="word-wrap: normal; word-break: normal;">ylabel('T')</span>
    
20. <span style="word-wrap: normal; word-break: normal;">zlabel('U')</span>
    
21. 
    
22. <span style="word-wrap: normal; word-break: normal;">% <wbr> <wbr>目标函数：</span>
    
23. <span style="word-wrap: normal; word-break: normal;">function <wbr>[c,f,s]=pdefun(x,t,u,du)</span>
    
24. <span style="word-wrap: normal; word-break: normal;">c=[1;1];</span>
    
25. <span style="word-wrap: normal; word-break: normal;">f=[0.024*du(1);0.17*du(2)];</span>
    
26. <span style="word-wrap: normal; word-break: normal;">temp=u(1)-u(2);</span>
    
27. <span style="word-wrap: normal; word-break: normal;">s=[-1;1].*(exp(5.73*temp)-exp(-11.46*temp));</span>
    
28. 
    
29. <span style="word-wrap: normal; word-break: normal;">% <wbr> <wbr>边界条件：</span>
    
30. <span style="word-wrap: normal; word-break: normal;">function <wbr>[pa,qa,pb,qb]=pdebc(xa,ua,xb,ub,t)</span>
    
31. <span style="word-wrap: normal; word-break: normal;">pa=[1;ua(2)];</span>
    
32. <span style="word-wrap: normal; word-break: normal;">qa=[1;0];</span>
    
33. <span style="word-wrap: normal; word-break: normal;">pb=[ub(1)-1;0];</span>
    
34. <span style="word-wrap: normal; word-break: normal;">qb=[0;1];</span>
    
35. 
    
36. <span style="word-wrap: normal; word-break: normal;">% <wbr> <wbr>初值条件：</span>
    
37. <span style="word-wrap: normal; word-break: normal;">function <wbr>u0=pdeic(x)</span>
    
38. <span style="word-wrap: normal; word-break: normal;">u0=[1;0];</span></div><div></div>

复制代码

想得到x为定值，比如x=0.2时，U1和U2随时间的变化曲线。

因为x=0.2在位置中的第5列，所以

1. <p style="margin-bottom: 16px; border: 0px; list-style: none; word-wrap: normal; word-break: normal;">figure
   
2. U1t <wbr>= <wbr>sol(:,5,1)
   
3. plot(t,U1t)
   
4. title('The <wbr>solution <wbr>of <wbr>u_1 <wbr>t')</p><div></div>

复制代码

转自：http://blog.sina.com.cn/s/blog_3ecbcc070101b4ei.html