# Analytic Solution Wave Equation

1. Nov 18, 2015

### leonmate

1. The problem statement, all variables and given/known data

Plot the solution at times t = 0, t = 0.25 and t = 0.5. Based on your knowledge of the general solution of the wave equation, the behaviour you see here, and the initial data profile, what is the analytic solution u(x, t) to this problem? (In deriving the analytic solution, you do not have to take into account the periodic boundary conditions; assume an infinite computational domain.)

u(x,0) = exp(-((x)^2)/(2.*0.1^2)
du/dt = 0
du/dx = -100x*u(x,0)

Ok, so I've been solving this problem numerically using python and this is the plot I get (attached)

So now I need to work out the analytic solution from this and I really don't know what to do.

I was working with this earlier but Im not sure if its correct

u(x,t) = F(x)G(t)
d2u/dt2 = F(x) d2G/dt2(t)
d2u/dx2 = d2F/dF2 G(t)

Something along these lines
http://tutorial.math.lamar.edu/Classes/DE/TheWaveEquation.aspx

I have to get this question done and the deadline is 5pm today :O :O :O

#### Attached Files:

• ###### Fig5.png
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2. Nov 23, 2015