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cmagnomarin1-Visitor
1-Visitor
May 5, 2016
Question

How to iterate a cycle to converge

  • May 5, 2016
  • 7 replies
  • 4251 views

Hello everyone,

I'm trying to create a way to iterate several equations of a dual cycle, in which I mainly guess for to variables. At the end I recalculate the variable I guess for and substitute the new value for the guess values until I get and error of 0.001. Yet, I can really find a way to make it simple and professional. Can anyone help me out or suggest a way or share an example? I would really appreciated.

7 replies

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StuartBruff23-Emerald V
23-Emerald V
May 5, 2016

Christian Eduardo Magno Marin wrote:

Hello everyone,

I'm trying to create a way to iterate several equations of a dual cycle, in which I mainly guess for to variables. At the end I recalculate the variable I guess for and substitute the new value for the guess values until I get and error of 0.001. Yet, I can really find a way to make it simple and professional. Can anyone help me out or suggest a way or share an example? I would really appreciated.

Do you need to iterate?  I would probably look at a Mathcad Solve Block for this kind of problem - look "solve block" up in help.

If you do need to iterate, then it would be helpful if you could post your worksheet, as that means the Community could offer more specific and tailored advice.

Stuart

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    LucMeekes23-Emerald IV
    23-Emerald IV
    May 5, 2016

    Here's an example of Newton's iteration method to find a square root.

    Success!
    Luc

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      -MFra-21-Topaz II
      21-Topaz II
      May 5, 2016

      Certainly, will be useful the following two examples. In the first, a transcendental equation is solved with the iterative algorithm of Newton. In the second one it solves a system of equations with the same iterative method but in several variables.

      Greetings

      F.M.

      iterations.jpg

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        cmagnomarin1-VisitorAuthor
        1-Visitor
        May 6, 2016

        Thanks StuartBruff, @LucMeekesand F.M.  for the suggestions. I’m gona try them right now.


          Okay StuartBruff, this is what I have at hand. I’m presented with a problem where I have a 6 cylinder CI engine and I’m given some data and a graph. The first part of the problem which I’m stuck on, is that I got to analyze the cycle of the engine, dual cycle. To initiate the cycle, I need to guess the value of x­r and T1 and calculate every state. At the end, I use the data from the exhaust state and I calculate x­r and T1. With the new xr­, I calculate the error and it must be at least an error of 0.001%, if not I need to replace the calculated values with the guess and start again. Attach is the worksheet. With another program I got that the converging values would be T1=311.8 K and xr=0.01594, but I would like to develop the calculations in Mathcad that is why I’m trying to work it out. And again I appreciate any suggestions colleagues. ‌

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        RichardJ19-Tanzanite
        19-Tanzanite
        May 6, 2016

        See the attached worksheet. The solve block at the end does your iteration for you.

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          cmagnomarin1-VisitorAuthor
          1-Visitor
          May 7, 2016

          Thanks @Richard Jackson, it is very helpful.

          But can you be kind to explain how does it work? Well how does it take the first calculated xr and T1 and recalculates? I mean, the whole time that I tried, I thought that I needed to put in the solve block all the equations that depended on the two variables. But I see that you only had to specified the variables that depended on xr and T1 and just on the solve block it was only needed to put the equations that calculate xr and T1. Also if I want the answer of a 5% error how would I specify that? Would I only have to change the default TOL? Also is there a way to see how many times does it iterate and the values of those iterations? Thanks in advance.

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