% Usage: y = heunstep(f,a,b,ya,n)
% One step of Heun's (or 'explicit trapezoid') method for initial value problems
%
% Input:
% f - Matlab inline function f(t,y)
% t - initial time
% x - initial condition
% h - stepsize
%
% Output:
% y - computed solution at t+h
% 
% Examples:
% y=heunstep(@myfunc,0,1,0.1);          here 'myfunc' is a user-defined function in M-file
% y=heunstep(inline('sin(y*t)','t','y'),0,1,0.1);
% f=inline('sin(y(1))-cos(y(2))','t','y');
% y=heunstep(f,0,1,0.1);

function y = heunstep(f,t,x,h)
g = f(t,x);
z = x + h * g;
y = x + 0.5 * h * ( g + f(t+h,z) );