topic Re: How to solve this non-linear system of eq? in Mathcad

How to solve this non-linear system of eq?

Cornel — Mon, 27 May 2024 11:24:24 GMT

Hi,

How to solve this non-linear system of equations:

Re: How to solve this non-linear system of eq?

Werner_E — Mon, 27 May 2024 12:46:35 GMT

You could use symbolic evaluation

But you can't evaluate the functions numerically because LambertW is a symbolic only function.

So you would have to resort to the numerics

Re: How to solve this non-linear system of eq?

Cornel — Mon, 27 May 2024 13:23:29 GMT

This is:

Now, how to find this?

And this:

Re: How to solve this non-linear system of eq?

Cornel — Mon, 27 May 2024 13:36:29 GMT

Do you have any idea why V2 and V3 should not depend also on t, like V1(t)? Initially I was expected/thought that also V2 and V3 should depend on t in the solve block like V1(t): V2(t), V3(t), but it seems that V2 and V3 in solve block should not put to depend on variable t like V1(t).

This not work:

I see that as you have posted firstly above works: this work

Re: How to solve this non-linear system of eq?

Cornel — Mon, 27 May 2024 14:14:52 GMT

I put also the circuit used in this topic for history purpose.

Re: How to solve this non-linear system of eq?

Werner_E — Mon, 27 May 2024 14:41:46 GMT

@Cornel wrote:

Do you have any idea why V2 and V3 should not depend also on t, like V1(t)?

They obviously do - otherwise you would just see constant functions when you plot. But "find" will only find numeric values, simple variables like V2 and not expressions like V2(t). Find looks for variables, not for functions!

You may provide the guess values for V2 and V3 just once (for the whole range of t) as I did or you may provide them as arguments of the function "sol" as you did. The latter would be necessary if you need to provide different guesses for different values of t which seems not to be the case here.

Re: How to solve this non-linear system of eq?

Werner_E — Mon, 27 May 2024 15:03:58 GMT

Re: How to solve this non-linear system of eq?

Cornel — Mon, 27 May 2024 15:25:13 GMT

Good, thank you. I think it's ok for now.

Re: How to solve this non-linear system of eq?

Werner_E — Mon, 27 May 2024 15:25:44 GMT

@Cornel wrote:

Good, thank you. But attached also the Mathcad Prime file to be here.

Opened your sheet with P10 and have not saved what I did. Do you experience any problems in retyping it?

Time for maximum value can be derived similar to the other thread and is shown for V3 at the top of the pic I posted here.

I found also another way: based on this

Sure, there are many ways to skin a cat 😉

Use whatever seems most appropriate to you.

Re: How to solve this non-linear system of eq?

Cornel — Mon, 27 May 2024 15:27:57 GMT

@Werner_E wrote:

Opened your sheet with P10 and have not saved what I did. Do you experience any problems in retyping it?

It's ok.

Time for maximum value can be derived similar to the other thread and is shown for V3 at the top of the pic I posted here.

I realized this after I requested you to do. But it;s ok now.