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M
ME_102554451-Visitor
1-Visitor
March 23, 2022
Question

Multiple ODE's in MathCad

  • March 23, 2022
  • 5 replies
  • 6477 views

Hi guys,

 

I have a question..

I modelled a 4th oder ODE in MathCad which works smoothly..

But when I tried to upgrade the script into (a system of ODE’s) 3 or 4 ODE’s, I couldn’t get it well working.

 

Note that I checked the boundary/matching conditions and they are correct. So something else could be wrong.

 

I’ve included the file in the mail.  

 

Would you like to help me here?

 

Thanks in advance!

 

5 replies

V
24-Ruby IV
ValeryOchkov24-Ruby IV
24-Ruby IV
March 25, 2022

The Odesolse finction cannot work with a boundary problem.

For this there are others tools. The Shot method for example (a programming). Or the bvalfit etc function.

  

 

M
ME_102554451-VisitorAuthor
1-Visitor
April 8, 2022

Dear Valery,

Could you help me with an example?

I'm not sure how the bvalfit works..

Thnx in advance

V
24-Ruby III
VladimirN24-Ruby III
24-Ruby III
April 17, 2022

From "Help Center" - "Deriving Initial Conditions for an ODE": https://support.ptc.com/help/mathcad/r8.0/en/#page/PTC_Mathcad_Help/deriving_initial_conditions_for_an_ode.html 

A
AlanStevens19-Tanzanite
19-Tanzanite
April 28, 2022

Attached is an attempt using the shooting method.  I've split it into two sections; one from x = 0 to x = s1, and one from x = s1 to x = L, matching the specified boundary conditions at x = s1.

Unfortunately, it doesn't get one of the final boundary conditions correct (that for W``(L)).

Alan

 

 

 

    M
    ME_102554451-VisitorAuthor
    1-Visitor
    April 29, 2022

    Dear Alan,

    I would like to thank you very much for your help, at least I'm a step further now.

     

     

    M
    ME_102554451-VisitorAuthor
    1-Visitor
    May 11, 2022

    Hallo Alan and everyone,

     

    Firstly, thank u Alan and eveyone who gave his time for this.

     

    Idon't know how to work with guesses and I don't even understand it.

    But also a question, I thought I know the exact values for the boundary/matching conditions, so why do we need guess values?

    Maybe I lack the experience here, but previously I used to program similar models in Maple but here (in MathCad) it does'nt work..

     

    Any Idea?

     

    Thanks in advance

     

    W
    Werner_E25-Diamond I
    25-Diamond I
    May 11, 2022

    This solution might not be satisfactory as it does not use a solver for a differential equation, but at least its a solution.

     

    You are asking for two polynomials of fourth order which are zero at 0 and s1 resp. s1 and L, have their second derivative at 0 resp. L to zero and have matching first and second derivatives at the joint position s1.

    Actually this means 10 conditions for 10 variables (the coefficients of the polynomials) which you can either solve using the symbolic solver or using a numeric solve block. Of course, as we know the fourth derivative of both functions being q/EI we could set the coefficient of x^4 in both functions to q/(24 EI). But I decided to let Mathcad do the job 😉

    Here is what Mathcad came up with

    Werner_E_0-1652295973509.png

    As you can see, the necessary conditions are met (apart from minor numerical inaccuracies):

    Werner_E_2-1652296192498.png

     

    i still have no idea how to get odesolve to come up with this solution, though.

     

    MC15 sheet attached

      W
      Werner_E25-Diamond I
      25-Diamond I
      May 11, 2022

      So here is a method which uses odesolve - unfortunately still not the "natural" way.

      First we use a separate solve block with "odesolve" for U and for W and turn it into a function of the value d2 of the second derivative at x=s1.

      Werner_E_0-1652300534267.png

       

      The only condition not met when we calculate the functions using the same value for d2 is that we also want the first derivatives at s1 to match.

      So we define a function to calculate the difference of the first derivatives at s1 for any value of d2

      Werner_E_1-1652300621417.png

      and use it in a solve block with "find" to iterate the values of d2 until we arrive at a value where the first derivatives are equal.

      Werner_E_2-1652300674465.png

      Werner_E_3-1652300697082.png

      Wish it would work in one go basically the way you had set it up, but it looks like Mathcad isn't capable enough to do so. However, I would be happy to be proven wrong.

      Mathcad15 worksheet attached

       

        M
        ME_102554451-VisitorAuthor
        1-Visitor
        May 16, 2022

        Hi mate,

         

        How wonderful is this update..

        Thanks so much for your time and efforts 

        I'll check it and let u know.

        ME_10255445_1-1652698980886.jpeg

         

        Thx,

         Mohamed 

        L
        LucMeekes23-Emerald IV
        23-Emerald IV
        May 20, 2022

        With reference to https://community.ptc.com/t5/Mathcad/Toolbox-Solving-Ordinary-Differential-Equations-symbolically/m-p/689336#M192090

        Your system of 2 ODE's can be solved as follows:

        LucMeekes_0-1653059279080.png

        LucMeekes_1-1653059293827.png

        LucMeekes_2-1653059303554.png

        LucMeekes_3-1653059311780.png

        LucMeekes_4-1653059321816.png

        LucMeekes_5-1653059331906.png

        LucMeekes_6-1653059356880.png

        Note that the value of d2 is:

        LucMeekes_7-1653059409742.png

        which corresponds to what @Werner_E found.

         

        If you want to run this in Mathcad 15, be sure to take the proper LODEsolve reference file,

        you need to replace the LODEsolve.mcd with LODEsolve.xmcd

         

        Success!
        Luc

         

          L
          LucMeekes23-Emerald IV
          23-Emerald IV
          May 20, 2022

          Oh, and in case you wonder if it can be done with three sections...

          Hoping/assuming I have set the proper initial/boundary conditions, here goes:

          LucMeekes_0-1653062112084.pngLucMeekes_1-1653062119103.pngLucMeekes_2-1653062131381.png

          LucMeekes_3-1653062139326.png

          LucMeekes_4-1653062165664.png

          LucMeekes_5-1653062189827.png

          LucMeekes_6-1653062217272.png

          And in case you're wondering about d2 and d3... they are 0.1 each. That is respectively:

          LucMeekes_7-1653062337284.png

           

          The Mathcad 11 file is attached again.

          Success!
          Luc

           

           

            M
            ME_102554451-VisitorAuthor
            1-Visitor
            June 7, 2022

            Dear Luc,

             

            Thank you very much for this amazing effort. I appreciate it 

             

            Just one issue.. when I download your files, they don't run (calculate). That graph above doesn't plot any outcome! 

            I see the screenshot you included, so I know it should work but maybe it has to do with the version I'm working with (MathCad 15)..

             

            Any idea how I can get out of this dilemma?

             

            Thanks in advance 🙂 

             

            L
            LucMeekes23-Emerald IV
            23-Emerald IV
            June 7, 2022

            Yes. How about pressing the [F9] key every now and then, to calculate the sheet up to the point where it's being displayed. Or press [Ctl-F9] to calculate the entire sheet...

            I generally have Autocalculation switched OFF in my files. That way I can edit the expressions without being hampered by Mathcad trying to calculate every change I make, and slowing down my editing.

             

            Success!
            Luc

             

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