Using fsolve to solve nonlinear equations that have user-defined functions

Hi there,

I have a problem using fsolve to solve nonlinear equations that have my own functions. See the code below:

options = optimset('TolFun', 1e-10, 'Display', 'iter', 'MaxFunEvals', 1e10, 'MaxIter', 1e9, 'Algorithm', 'Levenberg-Marquardt');
w=2;
h=1;
l=20;
n=0;
M=0;
E=70*10^9;
I= 1/12*h^3*w;
L=l;
UnknownGuess = rand(1,1);
[Unknowns, fval,exitflag] = fsolve('kkk', UnknownGuess, options,n,M,E,I,L);
P = Unknowns(1);
%%%%%%%%%%%%
function F = kkk(Unknown,n,M,E,I,L)
F(1)=XX([n,Unknown(1),E,I,M,L])+2;
end
%%%%%%%%%%%%
function Y=XX(X)
n=X(1,1);
P=X(1,2);
E=X(1,3);
I=X(1,4);
M=X(1,5);
L=X(1,6);
xmesh = linspace(0,L,100);
solinit = bvpinit(xmesh, @guess);
sol = bvp4c(@bvpfcn, @bcfcn, solinit);
fitobject = fit(sol.x(1,:)',sol.y(1,:)','poly9');
fun1 = @(x) cos(fitobject.p1.*x.^9 + fitobject.p2.*x.^8 + fitobject.p3.*x.^7 + fitobject.p4.*x.^6 + fitobject.p5.*x.^5 + fitobject.p6.*x.^4 + fitobject.p7.*x.^3 + fitobject.p8.*x.^2 + fitobject.p9.*x + fitobject.p10);
Y=integral(fun1,0,L)-L;
function g = guess(x)
g = [sin(x)
     cos(x)];
end
function dydx = bvpfcn(x,y)
dydx = [y(2)
       -P/E/I*(cos(y(1))+n*sin(y(1)))];
end
function res = bcfcn(ya,yb)
res = [ya(1)
       yb(2)-M/(E*I)];
end
end
%%%%%%%%%%%%%
                                        First-Order                    Norm of 
 Iteration  Func-count    Residual       optimality      Lambda           step
     0           2               4               0         0.01

No solution found.

fsolve stopped because the problem appears regular as measured by the gradient,
but the vector of function values is not near zero as measured by the
selected value of the function tolerance.

<stopping criteria details>

I have checked the conditions of fsolve, such as: the equation to be solved has to be continuous.etc..however, they all match.

I think I must have missed something or made a mistake somewhere in my script as 'kkk' along with the given conditions does have a solution:

XX([n,4.16*10^7,E,I,M,L]) is around -2

Can anyone help me?

Thanks in advance,

Ke

[Ke Wu]

@Alan Stevens Could you please take a look at it?

Thank you so much!

Ke

[Alan Stevens]

fsolve requires the optimisation toolbox, which I don't have, so I'm no use to you here I'm afraid!

[Ke Wu]

Haha Thanks anyway!