function y_2 = odeStep_rk4(x_1,y_1,h,deriv)
%y_2 = odeStep_rk4(x_1,y_1,h,deriv);
% A self-starting, simple, single Runge-Kutta 4th-order step function
%  x_1 --> initial independent variable (scalar, typically time)
%  y_1 --> initial dependent variable (vector)
%    h --> step size in x
%deriv --> function handle for derivative function (annonymous call
%          if derivatives are functions of parameters other than x & y)
%  y_2 <== final dependent variable; i.e., y(x_1+h) 

% (c) 2007 Curt A. L. Szuberla
% University of Alaska Fairbanks, all rights reserved

% ver 1.01
% 21 December 2007

% implementation of standard Runge-Kutta 4th-order formula
k_1 = h * deriv(x_1,y_1);                    % step w/ slope at start
k_2 = h * deriv(x_1 + h/2 , y_1 + k_1/2);    % step w/ slope in middle
k_3 = h * deriv(x_1 + h/2 , y_1 + k_2/2);    % same but using second result
k_4 = h * deriv(x_1 + h   , y_1 + k_3);      % step w/ slope at end
y_2 = y_1 + (k_1 + 2*k_2 + 2*k_3 + k_4)/6;   % weighted avg. of steps

return