Author Topic: Web Bonus Problem 2  (Read 1155 times)

Victor Ivrii

  • Administrator
  • Elder Member
  • *****
  • Posts: 2511
  • Karma: 0
    • View Profile
    • Personal website of Victor Ivrii
Web Bonus Problem 2
« on: January 14, 2015, 09:20:14 AM »
Solve
\begin{align}
&(t^2+1)u_{tt}+tu_t-u_{xx}=0,\label{eq-1}\\[3pt]
&u|_{t=0}=0, \qquad u_t|_{t=0}=1.\label{eq-2}
\end{align}
Hint: Make a change of variables $x=\frac{1}{2}(\xi+\eta)$, $t=\sinh (\frac{1}{2}(\xi-\eta))$ and calculate $u_\xi$, $u_\eta$, $u_{\xi\eta}$.
« Last Edit: January 27, 2015, 09:54:48 PM by Victor Ivrii »

Yiyun Liu

  • Full Member
  • ***
  • Posts: 15
  • Karma: 0
    • View Profile
Re: Web Bonus Problem 2
« Reply #1 on: January 27, 2015, 09:39:39 PM »
pro,I think there is a type error of the hint you provide, should x=(xi+eta)/2 instead of xi=(xi+eta)/2 ?
thx

Thanks, corrected. V.I.
« Last Edit: January 27, 2015, 09:55:39 PM by Victor Ivrii »