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JohnRudnicki15-Moonstone
15-Moonstone
November 16, 2021
Question

ODE Solvers Won't Solve

  • November 16, 2021
  • 2 replies
  • 1816 views

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.

2 replies

V
VladimirN24-Ruby III
24-Ruby III
November 17, 2021

What version of Mathcad are you using?

J
JohnRudnicki15-MoonstoneAuthor
15-Moonstone
November 18, 2021

I am using MathCad 14. I post with MathCad 11 so that Luc can help if he wants to.

L
LucMeekes23-Emerald IV
23-Emerald IV
November 17, 2021

I get to t=0.67. :

LucMeekes_0-1637148206876.png

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

    J
    JohnRudnicki15-MoonstoneAuthor
    15-Moonstone
    November 18, 2021

    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

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