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I have two ode's that have a parameter. When I set the parameter to zero some (but not all) the solvers give results that might be reasonable. But, if I make that parameter a very small number, none of the solvers work even though this would not seem to make the equations parthological. Does anyone have some insight to what is going on?
Thanks.
What version of Mathcad are you using?
I am using MathCad 14. I post with MathCad 11 so that Luc can help if he wants to.
I get to t=0.67. :
for higher values of tend, the error message is: "Found a number with magnitude greater than 10^307 while trying to evaluate this expression". I guess it's related to v(t) running skyhigh
What is the 0 doing in your expression for dTau; should it be Theta? Not that it helps, though: With Theta in that position, I get a solution only up to t=0.1.
Success
Hi Luc
Thanks. That was helpful. I anticipated spikes, but not so early. I should have investigated shorter time intervals. With AdamsBDF I get up to 0.8 although all the other solvers fail. Increasing eta which is a kind of damping parameter might help. I haven't looked at this yet but I cannot make it unrealistically large. I do not get a helpful error message like you did. The ones I get are different and less helpful: "this value must be real," "the return value of the function must match the problem size", "this problem does not converge to a solution". A difference between MC 11 and MC 14? I remember that we communicated about this before.
The zero in dtau should be there. I modified the worksheet from one that looks at a different case. Instead of eliminating the number that went into there, I just made it zero.
Just case you are interested, the equations describe a spring block model that uses a particular type of friction that has been documented in many experiments on rocks. The friction depends on the velocity v and a state variable theta that reflects the evolving characteristics of the friction surface. The spikes correspond to model earthquakes.
Thanks for taking a look at it.
John