I keep getting this error, " Failure in initial objective function evaluation. FSOLVE cannot continue."

Hi, currently I trying to solve for a system of nonlinear equations (5 equatios in total).

Here is my function part

% Coeffecient
M1 = 0.5;
M2 = 0.75;
M3 = 0.95;
M4 = 1.102;
M5 = 1.102;
K = 1;
Kc = 1;
Kk = 3;
KR = 0.95;
G = 0.001; 
GR = 0.1;
Gc = 0.005;
B = 0.15;
A= 1;
w= 1:0.1:2;

%Set up equation
    function F = MyFunction(x)
    F(1 )= x(1).*(-M1.*(w.^2) + K + Kc +KR + G.*1i.*w) - (A.*(exp(1i.*w)) + Kc.*x(4) + KR.*x(3));
    F(2) = x(2).*(-M2.*(w.^2) + K + Kc +KR + G.*1i.*w) - (A.*(exp(1i.*w)) + Kc.*x(5) + KR.*x(3));
    F(3) = x(3).*(-M3.*(w.^2) + 2.*kk + GR.*1i.*w) - (KR.*(x(1) + (x(2))));
    F(4) = x(4).*(-M4.*(w.^2) + Kc + kk + Gc.*1i.*w) - B.*1i.*(w.^3).*((x(4)).^3) - A.*(exp(1i.*w)) - Kc.*x(1);
    F(5) = x(5).*(-M5.*(w.^2) + Kc + kk + Gc.*1i.*w) - B.*1i.*(w.^3).*((x(4)).^3) - A.*(exp(1i.*w)) - Kc.*x(2);
    
    end

Then I create a different file to call back to it

x0 = [1 1 1 1 1];
x = fsolve(@MyFunction,x0);

So the idea is to solve x1, x2, x3, x4, x5 as a function of w. But I have tried fixing w to 1 value, as well as move the coeffecient to the 2nd file. But I still could fix this message that MATLAB gave me " Failure in initial objective function evaluation. FSOLVE cannot continue"

Anybody have a way for me to fix this

Answer 1

[Navya Seelam]

fsolve fails to continue because the function MyFunction doesnot not have access to the variables (M1, M2, M3...). You can use global variables for MyFunction to work without errors.

global param 
param.M1 = 0.5;
param.M2 = 0.75;
param.M3 = 0.95;
param.M4 = 1.102;
param.M5 = 1.102;
param.K = 1;
param.Kc = 1;
param.Kk = 3;
param.KR = 0.95;
param.G = 0.001; 
param.GR = 0.1;
param.Gc = 0.005;
param.B = 0.15;
param.A= 1;
param.w= 1;
x0 = [1 1 1 1 1];
fun=@MyFunction;
x = fsolve(fun,x0);

function F = MyFunction(x)
    global param 
    F(1 )= x(1).*(-param.M1.*(param.w.^2) + param.K + param.Kc +param.KR + param.G.*1i.*param.w) - (param.A.*(exp(1i.*param.w)) + param.Kc.*x(4) + param.KR.*x(3));
    F(2) = x(2).*(-param.M2.*(param.w.^2) + param.K + param.Kc +param.KR + param.G.*1i.*param.w) - (param.A.*(exp(1i.*param.w)) + param.Kc.*x(5) + param.KR.*x(3));
    F(3) = x(3).*(-param.M3.*(param.w.^2) + 2.*param.Kk + param.GR.*1i.*param.w) - (param.KR.*(x(1) + (x(2))));
    F(4) = x(4).*(-param.M4.*(param.w.^2) + param.Kc + param.Kk + param.Gc.*1i.*param.w) - param.B.*1i.*(param.w.^3).*((x(4)).^3) -param.A.*(exp(1i.*param.w)) - param.Kc.*x(1);
    F(5) = x(5).*(-param.M5.*(param.w.^2) + param.Kc + param.Kk + param.Gc.*1i.*param.w) - param.B.*1i.*(param.w.^3).*((x(4)).^3) - param.A.*(exp(1i.*param.w)) - param.Kc.*x(2);
end

[Viet Tran]

Thank you for answering, this method works for me but is there a way I can keep w varying instead of fixing it to 1 value?

Answer 2

[Dhananjay Kumar]

Declare a 5x11 F in the beginning and use proper indexing on F like this:

F = ones(5,11);

F(1,:)= x(1).*(-M1.*(w.^2) + K + Kc +KR + G.*1i.*w) - (A.*(exp(1i.*w)) + Kc.*x(4) + KR.*x(3));

F(2,:) = x(2).*(-M2.*(w.^2) + K + Kc +KR + G.*1i.*w) - (A.*(exp(1i.*w)) + Kc.*x(5) + KR.*x(3));

F(3,:) = x(3).*(-M3.*(w.^2) + 2.*kk + GR.*1i.*w) - (KR.*(x(1) + (x(2))));

F(4,:) = x(4).*(-M4.*(w.^2) + Kc + kk + Gc.*1i.*w) - B.*1i.*(w.^3).*((x(4)).^3) - A.*(exp(1i.*w)) - Kc.*x(1);

F(5,:) = x(5).*(-M5.*(w.^2) + Kc + kk + Gc.*1i.*w) - B.*1i.*(w.^3).*((x(4)).^3) - A.*(exp(1i.*w)) - Kc.*x(2);