### Re: Assn 10

Backward Euler is order 1, BDF is order 4. Residual error: 10^-8

I run into machine precision problems with the BDF curve when my time step is smaller than 2^-13

My convergence plot:

Backward Euler is order 1, BDF is order 4. Residual error: 10^-8

I run into machine precision problems with the BDF curve when my time step is smaller than 2^-13

Backward Euler is order 1, BDF is order 4. Residual error: 10^-8

I run into machine precision problems with the BDF curve when my time step is smaller than 2^-13

i can't see any plots? does anybody else have this problem?

dan

dan

Dan Negrut wrote:i can't see any plots? does anybody else have this problem?

dan

I couldn't see any plots when I wasn't logged in. Once I logged in to post, then I could see the pictures. But because you are posting, you must be logged in, so I have no idea.

I'm having trouble with problem 4

I'm evaluating the g(xn,yn) using this matlab code

And the Jacobian using this code

I've checked both at least three times although I get the same answer if I turn the Jacobian off in fsolve

for alpha = beta = 1 I get this plot for x using bEuler

and this for fEuler

The x axis is not plotted correctly.

I feel like the forward euler is probably the correct solution but I can't figure out what could be wrong with my backward Euler.

could someone run their backward Euler with alpha = beta = 1 and at least confirm that one of the two plots are correct

I'm evaluating the g(xn,yn) using this matlab code

And the Jacobian using this code

I've checked both at least three times although I get the same answer if I turn the Jacobian off in fsolve

for alpha = beta = 1 I get this plot for x using bEuler

and this for fEuler

The x axis is not plotted correctly.

I feel like the forward euler is probably the correct solution but I can't figure out what could be wrong with my backward Euler.

could someone run their backward Euler with alpha = beta = 1 and at least confirm that one of the two plots are correct

Last edited by ME751James on Wed Apr 07, 2010 5:29 pm, edited 1 time in total.

Delta < 10^-7

steps from 2^-6 to 2^-12

steps from 2^-6 to 2^-12

Last edited by ME451Tyler on Wed Apr 07, 2010 6:10 pm, edited 1 time in total.

Rob Bradford wrote:Rob's Convergence Plot #5

can't see your plots, can see Tyler's.

dan

Here it is a second try. I'm not sure why you can't see it. I can (along with Tyler's). It's the same as everyone else's plot.

ME751James wrote:I'm having trouble with problem 4

I'm evaluating the g(xn,yn) using this matlab code

And the Jacobian using this code

I've checked both at least three times although I get the same answer if I turn the Jacobian off in fsolve

my bEuler is what you have.

is F the forces in the global reference frame? so [0 0 -9.81*mass]'

Jbar is simply a diagonal matrix filled with the value from 1/12*mass*4^2 right?

Jbar is simply a diagonal matrix filled with the value from 1/12*mass*4^2 right?

For number five, are we supposed to derive the coefficients for order 4 BDF? Or is the table in the notes accurate enough? I'm having problems with my BDF and I'm not sure if I'm supposed to do all of the work of solving the order 4 coefficients.

Here are my convergence plots. Note that below ~2^-11 I ran into machine precision issues... Above that limit though, i see the expected slopes.

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