Using fsolve for a set of complex equations

Dear all,

I am now using 'fsolve' to solve a set of nonlinear equations. The equations are very complex and it is difficult to directly write it out. So I hope to firstly assemble it.

dx2 = x2(n)-x(1);
dx1 = x(1);
K1 = k1*(sqrt(2)*(1-dx1)./(dx1.*sqrt((1-dx1).^2+1))-1./dx1+1);
K2 = k2*(sqrt(2)*(1-dx2)./(dx2.*sqrt((1-dx2).^2+1))-1./dx2+1);
K_step = [ K2, -K2;
          -K2, K1+K2];
X_step = [x2(n);x(1)];
F_step = [x(2);0];

Then the function to be solved is

fun = @(x) K_step*X_step-F_step;

So the variables appear before the fun @(x). How can I write my codes in this condition? Thank you so much.

Answer 1

[Torsten]

If you want to define K_step*X_step-F_step as a function handle, you will have to define all expressions involving components of x as function handles.

  dx2 = @(x)x2(n)-x(1);
  dx1 = @(x)x(1);
  K1 = @(x)k1*(sqrt(2)*(1-dx1(x))./(dx1(x).*sqrt((1-dx1(x)).^2+1))-1./dx1(x)+1);
  K2 = @(x)k2*(sqrt(2)*(1-dx2(x))./(dx2(x).*sqrt((1-dx2(x)).^2+1))-1./dx2(x)+1);
  K_step = @(x)[ K2(x), -K2(x);
                -K2(x), K1(x)+K2(x)];
  X_step = @(x)[x2(n);x(1)];
  F_step = @(x)[x(2);0];
  fun = @(x)K_step(x)*X_step(x)-F_step(x);

This looks (and is) very ugly.

So I suggest you define a function to compute K_step*X_step-F_step:

fun = @(x)xstep(x,x2,n,k1,k2)

function res = xstep(x,x2,n,k1,k2)
  dx2 = x2(n)-x(1);
  dx1 = x(1);
  K1 = k1*(sqrt(2)*(1-dx1)./(dx1.*sqrt((1-dx1).^2+1))-1./dx1+1);
  K2 = k2*(sqrt(2)*(1-dx2)./(dx2.*sqrt((1-dx2).^2+1))-1./dx2+1);
  K_step = [ K2, -K2;
            -K2, K1+K2];
  X_step = [x2(n);x(1)];
  F_step = [x(2);0];
  res = K_step*X_step-F_step;
end