I am trying to findout maximum value of a equation of two variable

an = 1500;
bn = 0.0022;
Mn = 0.024;
gn = 10^-15;
mu_n = 3;
syms x y real
eqns = Mn - mu_n*[1+exp(-an*(gn*(x + y)-bn))]
dx = diff(eqns,x);
dy = diff(eqns,y);
r= diff(eqns,x,2);
t= diff(eqns,y,2);
s= diff(dx,y);
sol = vpasolve([dx,dy])
subs(r,{x,y},{sol.x,sol.y})
subs(t,{x,y},{sol.x,sol.y})
subs(s,{x,y},{sol.x,sol.y})
A = r*t;
B = s^2;
if A>B 
    if r > 0
    disp('minima');
    else
        disp('maxima');
    end
elseif A < B
    disp('no minima & no maxima');
else
    disp('no solution');
end
subs(eqns,{x,y},{sol.x,sol.y})

[KSSV]

Okay..you can find....but what is the problem?

[Rik]

For those without the curve fitting toolbox, this strategy works for most function (although I suspect it failed here):

an = 1500;
bn = 0.0022;
Mn = 0.024;
gn = 10^-15;
mu_n = 3;
eqns = @(x,y) Mn - mu_n*(1+exp(-an*(gn*(x + y)-bn)));
x0=1;y0=1;
fit_result=fminsearch(@(a) -eqns(a(1),a(2)),[x0 y0])
x=fit_result(1);y=fit_result(2);

[NEELU GUPTA]

Sir,my coding is working for most of the equation of two variable,easily gives me maxima and minima.but for this equation there are some error,i m not able to tackel the errors

[NEELU GUPTA]

In actual,this is my problem (Pi*,Pj*)= arg max{Mn}

[madhan ravi]

Are you sure the solution exists?

[NEELU GUPTA]

this is my algo (attachment file),for which i am trying equation like that, (Pi*,Pj*)= arg max{Mn-mu_n[1+exp(-an(gn(Pi+Pj)))]}

[NEELU GUPTA]

i need two points (Pi*,Pj*),Suggest me if there is another solution.

[NEELU GUPTA]

thanks to all for replying

Answer 1

[Walter Roberson]

subs() does not change the original variable unless you assign the result to the variable.