Mathematics · Numerical Methods
In order to numerically solve the ordinary differential equation dydt = -y for t > 0, with initial condition y(0) = 1, the following scheme is employed: yn+1 - ynΔt = -12(yn+1 + yn) Here, Δt is the time step and yn = y(nΔt) for n = 0, 1, 2, ... This implicit Crank-Nicolson numerical scheme will yield a solution with non-physical oscillations for Δt > h. The value of h is:
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