ode numerical answer with euler-method

hello i am trying to solve ode with Euler’s Method this state equtin x_dot=A*x+B*U

when x_dot=2x1,A=2x2,x=2x1,b=2x1,U=1x1 .

i dit it for one varbile but how do i do it when i have 2 varbles (meaning that i habe 2 solutions for x and not 1 sulotion for x )

Answer 1

[James Tursa]

You do it for vectors pretty much the same way you would do it for scalars. The main difference would be that you need to account for the fact that x is a vector if you are saving all of the intermediate results. E.g., something like this:

% set constants etc here
x = some initial value
t = some initial value
dt = some step size
n = number of steps to take
xresult = zeros(numel(x),n); % allocate the result variable
xresult(:,1) = x;  % save initial value
for k=2:n
    % if needed, update A, B, U here
    x_dot = A*x + B*U;  % calculate derivative
    x = x + x_dot*dt;  % take the Euler step
    t = t + dt;
    xresult(:,k) = x;  % save this intermediate result
end