CFD Online Discussion Forums

CFD Online Discussion Forums (
-   Main CFD Forum (
-   -   implicit vs explicit (

pXYZ April 21, 2006 05:59

implicit vs explicit

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)

Tom April 21, 2006 07:15

Re: implicit vs explicit
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.

Steve April 21, 2006 09:48

Re: implicit vs explicit
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.

All times are GMT -4. The time now is 09:01.