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function [t,x] = heun(field, t0, T, x0, h)
%HEUN Implements the Heun one-step ODE solver
%
% Parameters:
% field -- Right hand side function of ODE system: x'=f(t,x)
% t0 -- Initial time
% T -- End time (T > t0)
% x0 -- Initial value
% h -- Size of time step (h <= T-t0)
%
% Outputs:
% t -- [t0; t-0+h, t0+2*h; ...; t0+i*h; ...]
% x -- Matrix containing numerical solution, with each row the value of x
% at each time step
n = ceil((T-t0)/h);
t = t0+h*(0:n).';
x = ones(n+1,length(x0));
x(1,:) = x0;
for i=1:n
k1 = feval(field, t(i), x(i,:).');
k2 = feval(field, t(i)+h, x(i,:).'+h*k1);
x(i+1,:) = x(i,:).' + h*(k1+k2)/2;
end
