Home / Questions / The wave equation ? 2u(x, t)/ ?t2 = ? 2u(x, t) /?x2 can be written as u? = v v? = w ' w? = v'
The wave equation ∂ 2u(x, t)/ ∂t2 = ∂ 2u(x, t) /∂x2
can be written as u˙ = v
v˙ = w '
w˙ = v' ,
where w = u'
Write a code in python that solves the wave equation as above, on a grid from x = −1 to x = 1, with periodic boundary conditions, using the Euler method.
The initial data should be u(x, 0) = exp( − x^2/ 2σ^2)
u˙(x, 0) = 0
u' (x, 0) = −100xu(x, 0),
where σ = 0.1
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