% Usage: y = midpointstep(f,t,x,h)
% One step of the midpoint 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=midpointstep(@myfunc,0,1,0.1);          here 'myfunc' is a user-defined function in M-file
% y=midpointstep(inline('sin(y*t)','t','y'),0,1,0.1);
% f=inline('sin(y(1))-cos(y(2))','t','y');
% y=midpointstep(f,0,1,0.1);

function y = midpointstep(f,tx,h)
halfh = h/2;
z = x + halfh * f(t,x);
y = x + h * f(t+halfh,z);