implicit vs explicit

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 April 21, 2006, 05:59 implicit vs explicit #1 pXYZ Guest   Posts: n/a Hi, I have written a little program to solve an ordinary dfferential equation. The user can decide whether an explicit or implicit integration method is used. Looking on the results, I cannot see any advantage of the implicit scheme. What do you think about it? The mathematical bakground was: IMPLICIT: f(t+Dt) = f(t) + Dt* df/dt|_(t+Dt) EXPLICIT: f(t+Dt) = f(t) + Dt* df/dt|_(t)

 April 21, 2006, 07:15 Re: implicit vs explicit #2 Tom Guest   Posts: n/a Try using f(t+Dt) = f(t) + 0.5*Dt*( df/dt|_(t+Dt) + df/dt|_(t) ) and vary the timestep comparing the results. For an ode you'd should really look at explicit Runge-Kutta methods rather than your forward Euler step.

 April 21, 2006, 09:48 Re: implicit vs explicit #3 Steve Guest   Posts: n/a One way of looking at it is that if f(t) is mass say and therefore df/dt is mass flow, what happens if Dt*df/dt(t) is negative and higher in magnitude than f(t)? In the explicit scheme you'll get negative mass (bad!). In the implicit scheme the iterated estimate of df/dt(t+Dt) will prevent the negative mass. Explicit schemes assume that the grients at (t) are constant through the step. Implicit ones don't. Explicit schemes require small steps because of this.

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