need plot a graph using Euler's method for both numerical and analytical

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% Euler's Method
% Initial conditions and setup
h = (10); % step size
x = (0):h:(60); % the range of x
y = zeros(size(x)); % allocate the result y
y(1) = (2); % the initial y value
n = numel(y); % the number of y values
for i=1:n-1
pi = 3.1416
a = 2
r = 1
f = a + (2 - 0.4*a) * x / r^2 * pi
y(i+1) = y(i) + h * f;
end
plot (x,y,'b')
grid on
  4 Comments
Mpho Mokgotlo
Mpho Mokgotlo on 30 Oct 2022
Thank you for the help. tht ting is when I try to plot the graph it gives out error message like : unable to perform assignment because the left and right sides have a different number of element, so I was asking what should I do or change and how
Jan
Jan on 30 Oct 2022
@Mpho Mokgotlo: If you mention an error, post a copy of the complete error message. Seeing some parts of the message only is less useful, e.g. the readers do not know, in which line the error occurs.

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Answers (2)

Alan Stevens
Alan Stevens on 30 Oct 2022
Edited: Jan on 30 Oct 2022
f = a + (2 - 0.4*a) * x(i) / r^2 * pi; % x(i) not just x.
% Also take note of the other comments above.

Jan
Jan on 30 Oct 2022
h = 10; % step size
x = 0:h:60; % the range of x
y = zeros(size(x)); % allocate the result y
y(1) = 2; % the initial y value
n = numel(y); % the number of y values
a = 2;
r = 1;
for i = 1:n-1
f = a + (2 - 0.4 * a) * x(i) / r^2 * pi;
% ^^^
y(i+1) = y(i) + h * f; % I guess this line fails
end
plot (x,y,'b')
grid on
A cleaned version of your code. Alan Stevens' hint is included (please accept his answer).
You can solve such problems using the debugger. Type in the command window:
dbstop if error
and run the code again. Matlab stops at the problem and you can check the values of the used variables.
size(y(i+1)) % A scalar, of course
size(y(i) + h * f) % Not a scalar
size(f) % Same size as x!
You do not want x in the line to get the value of f, but only the element x(i).
Do you really mean: ... / r^2 * pi or .../ (r^2 * pi) ?

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