Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I am having trouble with figuring out what my initial conditions should be for a simple finite difference algorithm I wrote in Matlab.

Specifically, I'm trying to show that the regular 1-Dimensional wave eqt $$\frac{\partial u^2}{\partial t^2} = c^2\frac{\partial u^2}{\partial x^2}$$ Looks like diffusion with some drift, when the wave speed $c$ is chosen to randomly be $0$ or $1$ on every interval of length $\epsilon$. ( The point is to let the length of the intervals $\epsilon \to0$)

Normally for a simple equation I would simply have constant boundary conditions where $$u(x,0)=1$$ and watch the wave go on an interval $[0,1]$, but obviously if this is the case, the implicit finite difference equation becomes explicit, and I get nonsense as I mess around with $c$.

My question is, what would suitable initial conditions for this problem be?

(Also, pointing me in the direction of some literature that may help with this problem would be greatly appreciated)

share|cite|improve this question

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.