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Solve the nonlinear equations using a bisection method:

TT_11056782
6-Contributor

Solve the nonlinear equations using a bisection method:

TT_11056782_0-1715535916961.png

Solve it for Mathcad 15

7 REPLIES 7

You may use the symbolic "solve" command to solve these equations in Mathcad.

Or you may use a solve block with "find"

Or you may use the "root" function.

Look them up in the help, give one of them a try and if you experience problems then come back here and post your worksheets with your attempts.

I would advise against using the symbolic "solve". In case of your first function it would return only the trivial solution x=0.
Using one of the numeric methods you get the other two solutions as well if you provide appropriate guess values.

Werner_E_0-1715542484850.png

 

If you really need it to be done using the simple bisection method for trainings purposes in your education, you have to look up the method in your lecture notes. You should not need Mathcad to do so other than for plotting to find suitable start values and to evaluate the functions numerically to see where the sign changes.

Of course you could write a Mathcad function wich takes the function and two initial values as its arguments and returns a list of left and right boundary values (until a certain precision is achieved). If this is your goal, then make a start, give it a try and if you get stuck, come back here and post your worksheet with your attempts.

 

ppal
17-Peridot
(To:TT_11056782)

I take it you are looking for one solution where both cross the "X" axis at the same point .

ppal_1-1715552260793.png

 

Werner_E
24-Ruby V
(To:ppal)


@ppal wrote:
I take it you are looking for one solution where both cross the "X" axis at the same point .

??? There is no such 'solution' !!

0.55768... is not the same as 0.56871....

I guess you may be able to even see it in your plot if you zoom in enough.

ppal
17-Peridot
(To:Werner_E)

Depends on your tolerance settings - 

0.5 is best we can get to.
Werner_E
24-Ruby V
(To:ppal)


@ppal wrote:

Depends on your tolerance settings - 

 


No, it depends on the math and the two zeros are close, but they are definitely different. In other words - the graphs of the two functions have a couple of common points but none of them lies exactly on the x-axis.

The default tolerance setting (10^-3) is all thats necessary to get the two different solutions mentioned.

 


0.5 is best we can get to.

???

 

Try to use a solve block with both function forced to be zero for the same x value. It will fail for good reason (even Mathcads error message is wrong and not helpful as is unfortunately usual with solve blocks.

Werner_E_0-1715573317814.png

Here in detail:

Werner_E_1-1715573798244.png

I guess the question here is about two different tasks of homework ...

 

Hello @TT_11056782

 

It looks like you have some responses from some community members. If any of these replies helped you solve your question please mark the appropriate reply as the Accepted Solution. 

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Thanks,
Community Moderation Team.

lvl107
20-Turquoise
(To:TT_11056782)

Guessing,  maybe it is this :

Intersection Points of 2 Curves .PNG  

Regards.

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