How do I solve the nonlinear power equation?

Need to find out the value of β and n

V = [ 0 3.39E-05 6.77E-05 0.000102 0.000135 0.000169 0.000203 0.000237 0.000271 0.000305

del P = [ 14667 49641 95901 145331 195375 273565 402275 531670 648587 755000]

del Po = 12000

Q = 2.22E-7

Cb = 10

u = 0.000894

A = 1.88E-04

[James Tursa]

Are you trying to fit beta and n to the data? What is A?

[MOHAMMAD SHAIFUL AMIN]

Dear James,

Thanks for your kind concern.

A = 1.88E-04

yes, I am trying to fit the delP and V value to model equation. An then will analyze the model parametrs beta and n.

[MOHAMMAD SHAIFUL AMIN]

Dear James

thanks a lot

[Alex Sha]

Hi, MOHAMMAD, your problem may also considered as a fitting problem of implict function, the results are as below:

β 189182698.607589

n 0.402453367095041

[MOHAMMAD SHAIFUL AMIN]

Dear Alex,

Thanks for your kind concern? I am not good in Matlab. I tried to solve it by excel. My results were β = 2.2E6 and n= 0.74. Still now i am trying to write the code in Matlab.

Would you please share or send me the matlab codes?

[Alex Sha]

Hi, if think delP as dependent and V as independent, it seems to be impossible to rewrite your function as a standard explicit fitting type like: delP=f(V), so have to be treated as a fitting problem of implcit function, it is a difficult job for software like Excel, even not easy for Matlab.

[MOHAMMAD SHAIFUL AMIN]

In the literature I found the n value is from .6-.75. As I have the delP value, I use the excel solver by varying the beta. Then choose another n and try to do the curve fitting manually. That's why I am curious to see the mathlab codes and function.

Answer 1

[James Tursa]

One strategy:

• Move del Po to the left side
• Take ln( ) of both sides
• Put the ln(beta) and n*ln(del P) on one side and the other stuff on the other side
• Rewrite this in matrix form: M * [ ln(beta) ; n ] = other stuff
• Code the M matrix and other side stuff in MATLAB
• Use backslash to solve for ln(beta) and n