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ptc-49210951-Visitor
1-Visitor
January 29, 2013
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System of equations not converging due to exponential term

  • January 29, 2013
  • 2 replies
  • 9161 views

Hi, I am trying to solve a system of 3 equation by iteration 'n'. The system of equations is solved over a range 'x'. There is convergence to a solution over a certain part of the range of 'x' but no convergence over the other part. I believe the exponential term in one of the equations is generating a number that is too large for mathcad to handle. Is there any way to get around this problem? Perhaps some reworking of system of equations to modify the exponential term (logarithmic scale)? Or is there another way I could go about solving this system of equations? Thanks, Jon (Please see the attached file)

Best answer by AlanStevens

If it's the infinite n solution you are actually interested in then a a Given ... Find solve block is probably a better approach - see attached (I've only included the Case 2 values, but it works ok on the Case 1 values, reproducing your large n values of J, deltaC etc.).

Alan

2 replies

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AlanStevens19-Tanzanite
19-Tanzanite
January 30, 2013

What range of x is it not converging over? Your equations all seem to work ok for me (but perhaps you had limited the range). Some of your graphs look like solid colour simply because there are so many lines jumping rapidly between two values. You can overcome this by selecting 'no lines' in the plot trace.

See attached.

Alan

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ptc-49210951-VisitorAuthor
1-Visitor
January 30, 2013

Thank you Alan. The solution is not converging over the range of about 0<x<550. I have included a graph for x<550 and for x>550. You will see that in the latter case the solution converges to a single value rather than bouncing. As a result of the values bouncing back and forth, the solution that is being generated is non linear. I have updated the file to show how the solution should behave - linearly. Any help on how to get the solution to converge to a single value over the whole range of x would be very helpful. Thanks!

S
StuartBruff23-Emerald V
23-Emerald V
January 30, 2013

How do you know it's supposed to converge rather than oscillate over that range? I note that you've set one of the C constants to zero - is it meant to be zero in the actual base equations (it certainly runs into numerical problems if set to the order of the other constant!)?

Stuart

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ptc-49210951-VisitorAuthor
1-Visitor
March 20, 2013

Thanks for all your help. I'm going to try to approach the problem from a different angle and perhaps that will help. To limit the complexity I am going to consider just 1 value of x and march that scenario forward through i. I'm posting a new thread with this... Thanks!

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