What is the solution to the IBVP PDE $u_{tt} = u_{xx}$, $-\infty < x < \infty$ $0 < t < \infty$ ICs u(x,0) = e^{-x^{2}} u_{t}(x,0) = 0?
回答 (1)
2015-03-13 3:46 am
Use D'Alembert's solution with c = 1, g(x) = e^(-x^2) and h(x) = 0:
Link:
http://en.wikipedia.org/wiki/D%27Alembert%27s_formula
So, u(x, t) = (1/2) [e^(-(x - t)^2) + e^(-(x + t)^2)].
I hope this helps!
Link:
http://en.wikipedia.org/wiki/D%27Alembert%27s_formula
So, u(x, t) = (1/2) [e^(-(x - t)^2) + e^(-(x + t)^2)].
I hope this helps!
收錄日期: 2021-04-21 01:31:11
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20150312112406AAkiMaz