How to plug x^2+y^2 in to euler's Method

Question:Use a numerical solver and Euler's method to obtain a four-decimal approximation of the indicated value. First use

h = 0.1

and then use

h = 0.05.

y' = x^2 + y^2, y(0) = 3; y(0.5)

code:

% MATH 282  
% Text: Differential Equations with Boundary-Value Problems, 9th Ed.  
% by Dennis Zill 
% Section 2.6, p.78, EXAMPLE 2 
clearvars 
format long
y(1) = 1; 
x(1) = 1; 
f(1) = x.^2.*(1) + y.^(2).*(1);
h = 0.1; 
for i = 2:6 
    x(i) = x(i-1) + h; 
    y(i) = y(i-1) + h*f(i-1); 
    f(i) = x.^(2).*(i)+y.^(2).*(i); 
end 

Unable to perform assignment because the left and right sides have a different number of elements.

x 
y 

Answer 1

[Paul]

Hi Michael,

Focusing only on the error message ... this line is the source of the error

    f(i) = x.^(2).*(i)+y.^(2).*(i); 

f(i) is a single element of f, but x and y both grow on each iteration through the loop. When x and y both have two elements, then the right hand side of the assignment has two elements, which can't be assigned to the single-element left hand side.