Solve a numerical function

I am trying to solve a numerical equation with three unkonown values Ge, G and t , thse values will be approximated by fitting the curve with the from equation (Gp) to the following data obtained.

This means that is possible to make a curve approximation in order to know the values of the G anf t terms, depending on the number of terms desired for the sum.

I would really appreciate if someone could help me please. Here is the code and the data:

clear all, close all

data1=[0.010931641 0.011369615 0.012298683];

data2=[691.5802655 719.3455778 778.7159258];

Gp=data2(1); wp=data1(1);

for i=1:11

Gp=Ge+(G(i)*wp^2*t(i)^2)/(1+wp^2*t(i)^2)

end

[Sam Chak]

You have 3 unknown variables, but only 1 equation to describe the relationship. Can you provide more information about the problem?

Gp = Ge + (G*wp²*t²)/(1 + wp²*t²)

(Gp – Ge)*(1 + wp²*t²) = G*wp²*t²

(Gp – Ge)*(1/(wp²*t²) + 1) = G

[Walter Roberson]

It is a curve fitting problem. You can solve for three variables if you have 3 or more points, each of which generates an implicit equation.

[issam BEN SALAH]

I already have an experimental curve, Gp as a function of w of which I tried to determine these variables by fitting it with this equation.

How can I solve this problem of fitting curve.

Answer 1

[Sam Chak]

Hi Issam

From the advice of Mr. Roberson, you can create 3 equations from the data points:

691.5802655 = Ge + (G*0.010931641²*t²)/(1 + 0.010931641²*t²);
719.3455778 = Ge + (G*0.011369615²*t²)/(1 + 0.011369615²*t²);
778.7159258 = Ge + (G*0.012298683²*t²)/(1 + 0.012298683²*t²);

and then solve them simultaneously to obtain the solutions for the 3 variables:

Ge ≈ 260.642
G  ≈ 2166.56
t  ≈ ±45.5822

[issam BEN SALAH]

Hi Sam,

Please is there any code on Matlab to solve this equation for 11 variables.

Thanks in advance

[Sam Chak]

Hi Issam

If you have 11 equations (required to solve for 11 variables), then you can use the code involving the fsolve function as shown here:

https://www.mathworks.com/help/optim/ug/fsolve.html#butbm05-1

Else, you can consult with Mr. @Walter Roberson if there is a better way for solving for 11 variables.

[issam BEN SALAH]

Hi Mr. Walter,

I tried to solve this problem by following this code to determined variables Ge G1 t1 t2 G2:

syms Ge G1 t1 G2 t2;
w=[0.010931641 0.011369615 0.012298683];
Gp=[691.5802655 719.3455778 778.7159258];
E1= (Ge - Gp(1) + (G1*t1^2*w(1)^2)/(t1^2*w(1)^2 + 1)+(G2*t2^2*w(1)^2)/(t2^2*w(1)^2 + 1));
E11=(- Gp(1) + (G1*t1^2*w(1)^2)/(t1^2*w(1)^2 + 1)+(G2*t2^2*w(1)^2)/(t2^2*w(1)^2 + 1));
E2=(Ge - Gp(2) + (G1*t1^2*w(2)^2)/(t1^2*w(2)^2 + 1)+(G2*t2^2*w(2)^2)/(t2^2*w(2)^2 + 1));
E22=(- Gp(2) + (G1*t1^2*w(2)^2)/(t1^2*w(2)^2 + 1)+(G2*t2^2*w(2)^2)/(t2^2*w(2)^2 + 1));
E3=(Ge - Gp(3) + (G1*t1^2*w(3)^2)/(t1^2*w(3)^2 + 1)+(G2*t2^2*w(3)^2)/(t2^2*w(3)^2 + 1));
E33=(- Gp(3) + (G1*t1^2*w(3)^2)/(t1^2*w(3)^2 + 1)+ (G2*t2^2*w(3)^2)/(t2^2*w(3)^2 + 1));
sol = solve(E1,E11,E2,E22,E3,E33, Ge, G1, t1, G2, t2)

But it is giving me the error

sol =

Ge: [16x1 sym]

G1: [16x1 sym]

t1: [16x1 sym]

G2: [16x1 sym]

t2: [16x1 sym]

May you help me please

[Walter Roberson]

I only see two solutions.

In any case, why do you think that is an error?

syms Ge G1 t1 G2 t2;
w=[0.010931641 0.011369615 0.012298683];
Gp=[691.5802655 719.3455778 778.7159258];
E1= (Ge - Gp(1) + (G1*t1^2*w(1)^2)/(t1^2*w(1)^2 + 1)+(G2*t2^2*w(1)^2)/(t2^2*w(1)^2 + 1));
E11=(- Gp(1) + (G1*t1^2*w(1)^2)/(t1^2*w(1)^2 + 1)+(G2*t2^2*w(1)^2)/(t2^2*w(1)^2 + 1));
E2=(Ge - Gp(2) + (G1*t1^2*w(2)^2)/(t1^2*w(2)^2 + 1)+(G2*t2^2*w(2)^2)/(t2^2*w(2)^2 + 1));
E22=(- Gp(2) + (G1*t1^2*w(2)^2)/(t1^2*w(2)^2 + 1)+(G2*t2^2*w(2)^2)/(t2^2*w(2)^2 + 1));
E3=(Ge - Gp(3) + (G1*t1^2*w(3)^2)/(t1^2*w(3)^2 + 1)+(G2*t2^2*w(3)^2)/(t2^2*w(3)^2 + 1));
E33=(- Gp(3) + (G1*t1^2*w(3)^2)/(t1^2*w(3)^2 + 1)+ (G2*t2^2*w(3)^2)/(t2^2*w(3)^2 + 1));
sol = solve(E1,E11,E2,E22,E3,E33, Ge, G1, t1, G2, t2)

sol = struct with fields:
    Ge: [2×1 sym]
    G1: [2×1 sym]
    t1: [2×1 sym]
    G2: [2×1 sym]
    t2: [2×1 sym]

vpa(subs([Ge, G1, t1, G2, t2], sol))

ans = 

[issam BEN SALAH]

Thanks for the help Mr. Walter