Euler Method for vector function

I'm tring to apply Euler method to vector function and I'm facing error in the loop. How it can be fixed?

h=0.1;
n=5; 
yexact=@(x) [cos(x); sin(x); - sin(x); cos(x)]; % the exact function 

s = size(x);
rows = s(1);


% the loop for solve DE 
for j = 1: rows
    y = zeros(1 , rows);
    Y(1,:) = [1; 0 ; 0 ; 1];  %intial condition
    x = linspace(0,0.5,n+1);
for i=1:rows
    f = [-sin(i); cos(i); - cos(i); -sin(i)];   % y'= f
    y(i+1,: ) = y(i, :) + h * f(x(i),Y(i,:));   % Euler method
end

% apply Euler method to differnt step sizes 
hh(j) = h;
h = h/2;
n = (0.5)/h;

[Steven Lord]

What is the full and exact text of the warning and/or error messages you receive when you run this code? Please show all the text displayed in orange and/or red in the Command Window as they may be useful in determining what's going on and how to avoid the warning and/or error.

[Askic V]

From the code it can be seen that at least one end is missing, i.e. the for loop is not ended.

[Erm]

error in line16 which is corresponging to the loop

>> Euler2
Error: File: Euler2.m Line: 16 Column: 1
At least one END is missing. The statement beginning here does not have a matching end.

[Erm]

I end the loop and I have another error

Index in position 1 is invalid. Array indices must be positive integers or logical values.

Error in Euler2 (line 23)
    y(i+1, : ) = y(i,: ) + h * f(x(i),Y(i,:));

Answer 1

[Askic V]

It appears to me that you want this:

clear
clc
close all
% step size
h = 0.1;
% final time
Tf = 5;
x = 0:h:Tf;

yexact = {@(x) cos(x); @(x) sin(x);@(x) -sin(x); @(x) cos(x)}; % the exact function 
nr_functions = size(yexact,1);

% Solving y' = f(x)
funcs = {@(x) -sin(x); @(x) cos(x);@(x) -cos(x); @(x) -sin(x)};
% Initial conditions

y = zeros(nr_functions, numel(x));
y(:,1) = [1; 0; 0; 1];

for i = 1:nr_functions % loop goes through functions
    for j = 1:numel(x)-1 % loop for each particular function
        y(i, j+1) = y(i, j) + h * funcs{i}(x(j)); 
    end
end

% Plot results
for i = 1: nr_functions
   subplot(nr_functions,1,i);
   plot(x, y(i,:));
   hold on
   plot(x, yexact{i}(x));
   legend ('Euler method', 'Exact');
end