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 Hooman December 22, 2011 11:51

Problem with Backward Euler Results

Hi,

I have tried to solve a system of equations in the form:
dy1/dt = y1 +dt*f(y1,y2)
dy2/dt = y2 +dt*f(y1,y2)

using different schemes such as forward Euler and backward (implicit) Euler and Runge Kutta order 4. My results seem to be OK for the forward Euler scheme and Runge Kutta above a certain number of time steps (A). But for implicit Euler using A time steps, I get an error after a certain number of time steps (say A-100). I was wondering if anyone had any ideas of what the problem might be. I can't think of anything at all.

Thanks!

 otd December 23, 2011 17:44

[QUOTE=Hooman;336756]Hi,

I have tried to solve a system of equations in the form:
dy1/dt = y1 +dt*f(y1,y2)
dy2/dt = y2 +dt*f(y1,y2)

Do you perhaps mean f( ... ) for the first equation

and g( ... ) for the second equation?

 Hooman December 25, 2011 09:37

yes, that's what I meant. Sorry!

 Hooman December 29, 2011 12:53

Any ideas?

 Hooman January 1, 2012 11:59

I just realized that if I use really small time steps (much smaller than that of explicit euler) my reuslts become OK. I am now thinking it could be because I used forward euler to work out the initial RHS's at the new time step, to calculate the y1 and y2 at the new time steps.

 Hooman January 1, 2012 12:02

ooh I just realize that I have written the equations wrong here. They should be:
dy1/dt = f(y1,y2)
dy2/dt = g(y1,y2)

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