ode_RK4.m

function [t,y] = ode_RK4(f,tspan,y0,N,varargin)
    %Runge-Kutta method to solve vector differential eqn y’(t) = f(t,y(t))
    % for tspan = [t0,tf] and with the initial value y0 and N time steps
    if nargin < 4 || N <= 0, N = 100; end
    if nargin < 3, y0 = 0; end
    y(1,:) = y0(:)'; %make it a row vector
    h = (tspan(2) - tspan(1))/N; t = tspan(1)+[0:N]'*h;
    for k = 1:N
        f1 = h*feval(f,t(k),y(k,:),varargin{:}); f1 = f1(:)'; 
        f2 = h*feval(f,t(k) + h/2,y(k,:) + f1/2,varargin{:}); f2 = f2(:)';
        f3 = h*feval(f,t(k) + h/2,y(k,:) + f2/2,varargin{:}); f3 = f3(:)';
        f4 = h*feval(f,t(k) + h,y(k,:) + f3,varargin{:}); f4 = f4(:);
        y(k + 1,:) = y(k,:) + (f1 + 2*(f2 + f3) + f4)/6; 
    end
end