t=a:h:b;

I need to code an iteration for the below algorithm:

 % a,h,b,s are constants. 

t=a:h:b;y(0)=s;

    f(k)(x,t)=t(k)+y(k);

    y(k+1)=y(k)+h*f(k);

please help me how to use for loop for this iteration.

[James Tursa]

I assume that the statement y(0)=s is meant to imply that the initial value of y at the initial value of t (which is "a" in this case) is "s"?

This is just numerical integration using the Euler method.

Answer 1

[James Tursa]

An outline of the loop:

s = whatever
a = whatever
b = whatever
h = whatever

y = zeros(size(t));
y(1) = s;
for k=1:numel(t)-1
    f = ________;  % <-- you fill the blanks in based on your formula from above
    y(k+1) = _______;  % <-- you fill the blanks in based on your formula above
end

If you want to save each of the derivative values, then you can use f(k) in the loop instead of just f. (And also initialize f = zeros(size(t)) prior to the loop)