% Usage: y = rk4step(f,t,x,h)
% One step of Runge-Kutta method of order 4 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=rk4step(@myfunc,0,1,0.1);          here 'myfunc' is a user-defined function in M-file
% y=rk4step(inline('sin(y*t)','t','y'),0,1,0.1);
% f=inline('sin(y(1))-cos(y(2))','t','y');
% y=rk4step(f,0,1,0.1);

function y = rk4step(f,tx,h)
halfh = h / 2;
s1 = f(t, x);
s2 = f(t + halfh, x + halfh * s1);
s3 = f(t + halfh, x + halfh * s2);
s4 = f(t + h, x + h * s3);
y = x + (s1 + 2 * s2 + 2 * s3 + s4) * h / 6