Solving a nonlinear equation with time-varying parameters

Dear all,

I want to solve this nonlinear equation: (a*b*exp(-c*d))*exp(-x)+2*b -2*x-b=0,

where in each iteration of the algorithm the a,b,c,d change values.

So I set up the following algorithm

 Myfun = @(x, a, b,c,d) (a*b*exp(-c*d))*exp(-x)+2*b -2*x-b;
fun = @(x) Myfun(x,  a, b,c,d); 
 x0=0;
  options = optimoptions('fsolve','Display','none');
   A = fsolve(fun,x0,options);

Is this code correct the way I have written it? Is there an alternative faster way to solve this problem? Because I noticed that the above algorithm is very slow.

Thanks in advance

Answer 1

[Star Strider]

Since you are solving for a single parameter, the fzero function is an option, and in this simulation, faster:

v = mat2cell(rand(1000,4), ones(1,1000), ones(1,4));                            % Create Variable Cell Array

Myfun = @(x, a, b,c,d) (a*b*exp(-c*d))*exp(-x)+2*b -2*x-b;

options = optimoptions('fsolve','Display','none');
t00 = clock;
for k1 = 1:1000
    [a,b,c,d] = v{k1,:};
    A0(k1) = fsolve(@(x)Myfun(x, a, b,c,d),1,options);
end
t01 = etime(clock, t00);

t10 = clock;
for k1 = 1:1000
    [a,b,c,d] = v{k1,:};
    A1(k1) = fzero(@(x)Myfun(x, a, b,c,d),1);
end
t11 = etime(clock, t10);
fprintf(1,'\n\tfsolve time = %.3f s\n\tfzero time  = %.3f s\n\n',t01, t11)

  fsolve time = 5.001 s
  fzero time  = 1.062 s