Step size increment?

Hello! I am new to Matlab and this might be a very simple question but please try and help me out!

So basically, I have both initial value(k0) and w(k0), where w is a function of k. Now we can step to k1 = k0 + dk and we will have to use w(k0) as the initial guess to find w(k1) then, k2 = k1 + dk and w(k2) can be found from w(k1) so on.

I have set k as the following;

k0 = 1/2;
w(k0) = 1.4;
k= linspace(1/2, 2/3, 101);

I would like find w(k).

Thank you very much!

[Image Analyst]

What is the formula for w(k)? Or how does w(k+1) depend on w(k), the prior element?

[Angela Mehta]

I have made a function that's dependent on w and k (myf2(w,k)) and I ran the function under a for loop. Here's part of the code that does that;

Nx= 201;
Ny= 301;
k0 = 1/3; 
xa = 0;
xb = 5;,
ya = -3;
yb = 1;
%define x and y
x = linspace(xa, xb, Nx); %real part of w
y = linspace(ya, yb, Ny); % imag part of w


I = sqrt(-1);
for ix = 1:Nx
    for iy = 1:Ny
        z = x(ix) + I*y(iy);
        func = @(z) myf2(z,k0);
        funcp = @(z) myf2p(z,k0);
 
    end
end
fprintf("Initial guess:\n");
[xi,yi] = ginput(1);
r0 = xi + I*yi;
r = r0;
maxit = 10; % max no of interations
%Runs Newton method
for it = 1:maxit
    tol = 1e-16; %tolerance 
   
    r = newton(func, funcp, x0, tol, maxit);
    format long
    %fprintf("%12.12e \n", r); %12 digits
    %disp(['f(x) = ' num2str(func(r))]); % residal
end

fprintf("Root: (%12.12e, %12.12e)\n", real(r), imag(r));


%%%%This is where I want to set w(k0) = real(r)

I hope that answered your question! Thanks a lot!

Answer 1

[Walter Roberson]

k = linspace(1/2, 2/3, 101);
w = zeros(size(k));
w(k(1)) = 1.4;
for idx = 2 : numel(k)
    w(idx) = function_to_find_w_k(k(idx), w(idx-1));
end

[Angela Mehta]

Hello! I tried to use this code with my code, posted in the previous comment, I am getting an error when I set

w(k(1)) = real(r);

Error message: "Array indices must be positive integers or logical values."

I don't know the reason for it! Also apologies for setting w(k0)=1.4, I thought it might be easier that way.

Thank you very much!

[Walter Roberson]

k = linspace(1/2, 2/3, 101);
w = zeros(size(k));
w(1) = 1.4;
for idx = 2 : numel(k)
    w(idx) = function_to_find_w_k(k(idx), w(idx-1));
end