Problem with Backward Euler Results

Hooman · December 22, 2011, 11:51

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)

December 22, 2011, 11:51	Problem with Backward Euler Results	#1
Hooman Senior Member Join Date: Jun 2010 Posts: 111 Rep Power: 16	Hi, I have tried to solve a system of equations in the form: dy1/dt = y1 +dtf(y1,y2) dy2/dt = y2 +dtf(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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December 23, 2011, 17:44		#2
otd Member private Join Date: Mar 2009 Posts: 74 Rep Power: 17	[QUOTE=Hooman;336756]Hi, I have tried to solve a system of equations in the form: dy1/dt = y1 +dtf(y1,y2) dy2/dt = y2 +dtf(y1,y2) Do you perhaps mean f( ... ) for the first equation and g( ... ) for the second equation?

December 25, 2011, 09:37		#3
Hooman Senior Member Join Date: Jun 2010 Posts: 111 Rep Power: 16	yes, that's what I meant. Sorry!

December 29, 2011, 12:53		#4
Hooman Senior Member Join Date: Jun 2010 Posts: 111 Rep Power: 16	Any ideas?

January 1, 2012, 11:59		#5
Hooman Senior Member Join Date: Jun 2010 Posts: 111 Rep Power: 16	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.

January 1, 2012, 12:02		#6
Hooman Senior Member Join Date: Jun 2010 Posts: 111 Rep Power: 16	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)