function y_2 = odeStep_midPt(x_1,y_1,h,deriv)
%y_2 = odeStep_midPt(x_1,y_1,h,deriv);
% A self-starting, simple, single mid point (Runge-Kutta 2nd-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 (may be 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 1.0
% 21 December 2007

% implementation of standard Runge-Kutta 2nd-order formula
k_1 = h * deriv(x_1,y_1);                  % use slope at start to estimate
k_2 = h * deriv(x_1 + h/2 , y_1 + k_1/2);  % final point then take that  
y_2 = y_1 + k_2;                           % information to go half way and  
                                           % get a new slope for estimating
                                           % final point

return