I'm trying to implement Euler's Method on the following ODE, with initial condition [y1, y2] = [1, 3] and on the interval t in [0, 1]:
The exact solution is given as:
I currently have two different code as a way to go about solving this but I'm not sure which is correct/how to fix them. I'm really struggling to figure out where to go from here and any help/advice would be really appreciated!
function [y] = ForwardEulers(y0, t)
n = 2;
h = (t(2) - t(1)/n);
y = y0;
A = [-500.5, 499.5; 499.5, -500.5];
[V, D] = eig(A);
for t = 1:n
y(t) = y0 * (V * ((eye(n) + h * (D))^t) * inv(V));
x(t) = t * h;
end
plot(x, y)
end
function [y] = ForwardEulers2(y0, t)
n = 2;
h = (t(2) - t(1))/n;
A = [-500.5, 499.5; 499.5, -500.5];
for i = 1:n
y(i) = ((eye(n) + (h* A))^i) * y0;
end
end
