偏微分方程PDE
求解題過程
By trial and error, find a solution of the diffusion equation u_t = u_xx with the initial condition u(x,0) = x^2
PDE 偏微分方程 u_t = u_xx
2014-03-03 8:36 am
回答 (3)
2014-03-03 3:32 pm
✔ 最佳答案
Let U(x,t)=(a*x^2+b*x+c)+(d*t^2+e*t+f)a,b,c,d,e,f=ConstantsUx=2ax => Uxx=2aUt=2d*t+e=2a => d=0, e=2aU(x,0)=(ax^2+bx+c)+0=x^2=> a=1, b=c=0, e=2=> U(x,t)=x^2+2t+f.....ans
2014-03-03 9:19 am
The function u(x,t) = x^2+2t is a solution.
2014-03-06 6:00 am
收錄日期: 2021-04-30 18:32:56
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20140303000016KK00146