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Old   December 22, 2011, 11:51
Default Problem with Backward Euler Results
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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!
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Old   December 23, 2011, 17:44
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[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?
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Old   December 25, 2011, 09:37
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yes, that's what I meant. Sorry!
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Old   December 29, 2011, 12:53
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Any ideas?
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Old   January 1, 2012, 11:59
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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.
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Old   January 1, 2012, 12:02
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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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