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A
AshehadAl1-Visitor
1-Visitor
September 14, 2010
Question

Solving for variables - 3 equations; using newton's method & Jacobian

  • September 14, 2010
  • 4 replies
  • 8158 views

Hi there,

I am trying to solve 3 equations with 3 variables. The form of the equation is as follows:

F(x,y,z,t) , G(x,y,z,t) and H(x,y,z,t). I'm attaching mathcad file.

When t is known or fixed, say t=2 or t=3 etc, I can solve these three equations. See attached for the functions and t.

But, I don't know how to generalise it, i.e. when t has a range of values, say t = 1,2,3 and so on. I would be glad if someone can look into this program and help me. Once I know how to program it for the this case, I can then perhaps do it for nonlinear case.

Thanks,

Ashehad

4 replies

V
ValeryOchkov24-Ruby IV
24-Ruby IV
September 14, 2010

May be this help You:

http://twt.mpei.ac.ru/MAS/Worksheets/Newton_2.mcd

http://twt.mpei.ac.ru/MAS/Worksheets/Newton_3.mcd

A
AshehadAl1-VisitorAuthor
1-Visitor
September 14, 2010

Thanks Valery,

I managed to visit the site you mentioned. However, I still have the same problem. i.e. How to modify the program so that it can give all the solutions corresponding to different values of t. i.e. I'd like to have solutions in an array. In other words, referring to the file I attached, I'd like to have x(t), y(t) , z(t) for t say from 1, 2,3...100.

I want to avoid typing each value of t and then noting its solution. Can the program be modified? e.g.by including loops.

Thanks,

Ashehad

A
AlanStevens19-Tanzanite
19-Tanzanite
September 14, 2010

Here's another possible approach.

Alan

A
AshehadAl1-VisitorAuthor
1-Visitor
September 14, 2010

Hi Alan,

Thanks a lot indeed.

Cheers,

Ashehad

J
jeanGiraud1-Visitor
1-Visitor
September 15, 2010

Ashehad Ali wrote:

Hi there,

I am trying to solve 3 equations with 3 variables. The form of the equation is as follows:

F(x,y,z,t) , G(x,y,z,t) and H(x,y,z,t). I'm attaching mathcad file.

When t is known or fixed, say t=2 or t=3 etc, I can solve these three equations. See attached for the functions and t.

But, I don't know how to generalise it, i.e. when t has a range of values, say t = 1,2,3 and so on. I would be glad if someone can look into this program and help me. Once I know how to program it for the this case, I can then perhaps do it for nonlinear case.

Thanks,

Ashehad

I don't understand your proposition [don't worry , I don't have either !]. Your proposition is bi-equivoke in the sense that your first attempt a linear solve in terms of many methods. The last such linear method "rref" is not commonly used, though it introduces to solving 3 planes in the space. Next you switch your proposition to generalize the "non-linear case" . At this point, the non-linear case switches to "quadrics", thus involving the symbolic solve for 'z' while maintaining the full meaning of the quadric. It is then at this point that your proposition is rather confusing in term of the meaning of the quadric wrt to the parameter 't'. What I'm saying is that while the linear case is rather simple and understandable, the switch to the non-linear case might very well deviate from the mathematical meaning and its representation. In short: I have no background in such extension of the "quadrics"with variable parameter.

Cheers, can't help. [jmG]

J
jeanGiraud1-Visitor
1-Visitor
September 24, 2010

>But, I don't know how to generalise it, i.e. when t has a range of values, say t = 1,2,3 and so on.<

_______________________________

Don't understand the ranging of ' t '

Can you propose more examples

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