solve a system of ODE

Hi, this is explicit Euler method to solve a ODE

function [x,t]=euleroesplicito(fcn,t0,x0,h,tend) n = fix((tend-t0)/h)+1; t = linspace(t0,t0+(n-1)*h,n); x = zeros(n,1); x(1) = x0; for i = 2:n x(i) = x(i-1) + h*feval(fcn,t(i-1),x(i-1)); end plot(t,x);

How can I extend this method to solve a system of two or more equations? Thank you.

Answer 1

[Are Mjaavatten]

 function [t,x]=euleroesplicito(fcn,t0,x0,h,tend)
    n = fix((tend-t0)/h)+1; 
    t = linspace(t0,t0+(n-1)*h,n); 
    x = zeros(n,length(x0)); 
    x(1,:) = x0; 
    for i = 2:n 
        x(i,:) = x(i-1,:) + h*feval(fcn,t(i-1),x(i-1,:))'; 
    end
end

Note that I have reversed the sequence of outputs to make it conform to Matlab's ODE standard. Test on the equatiion for free fall:

 g = -9.81;
 [t,x] = euleroesplicito(@(t,x) [x(2);g],0,[10;0],0.01,1);
 plot(t,x(:,1));

[adriano romano]

Works! thank you!