Solve partial differential equation with the explicit method:
∂u
∂t = 2
∂
2u
∂x2
on the domain 0 ≤ x ≤ 3, t ≥ 0 with homogeneous Dirichlet boundary conditions u(0, t) =
u(3, t) = 0 and initial conditions u(x, 0) = −3 sin
2πx
3
. Use ∆x = 0.5, ∆t = 0.05. Carry
out three time steps (that is find the solution up to the time t = 0.15). Plot your solution
at each time step as a function of x.
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