Converting Euler ODE to the MATLAB code

Hey Everyone!

I have a question related to the Euler Method implementation. I have the following function:

(1)

I have written its main function code as:

function y = eulerfunction(func, t, y0)
    n = length(t);
    y = nan(length(y0), n);
    y(:,1) = y0(:);
    for k = 1:n-1
        h = t(k+1) - t(k);
        y(:,k+1) = y(:,k) + h*func(t(k), y(:,k));
    end
end

Now I am writing the remaining script.

y0 = [3,0];
h = 0.5;
t = 0;

% I am confused in this line that what to write in these square brackets according to the given equation (1)
f = @(t, y) [    ];

y = eulerfunction(f, t, y0)

Can you please help me to convert that f(t,y) in MATLAB Format? Like what to write in these brackets '[ ]' according to the f (t,y) in above equation (1):

f = @(t, y) [ ];

Any help will be really appreciated! Thanks alot in advance.

Answer 1

[Fabio Freschi]

f is an anonymous function

f = @(t,y)[-2*y(1)+y(2)+15*cos(t); 2*y(1)-y(2)];

note that your script is not correct, since t is the time vector used for the time integration and h is calculated inside the euler function. All in all

% initial value
y0 = [3,0];

% time vector
t = linspace(0,4*pi,100);

% anonymous function
f = @(t,y)[-2*y(1)+y(2)+15*cos(t); 2*y(1)-y(2)];

% solution
y = eulerfunction(f, t, y0);

% plot
figure,plot(t,y);

% your euler method
function y = eulerfunction(func, t, y0)
    n = length(t);
    y = nan(length(y0), n);
    y(:,1) = y0(:);
    for k = 1:n-1
        h = t(k+1) - t(k);
        y(:,k+1) = y(:,k) + h*func(t(k), y(:,k));
    end
end

[Haider Ali]

thats perfect! thanks alot for this urgent help.