% Runge-Kutta method for solving the differential equation
% y' = t^2-y with y(0)=1 for t in the range from 0 to 2

h = 0.05;		% stepsize
tstart = 0;		% smallest t value
tlast = 2;		% larest t value
ystart = 1;		% y(0) =1 


y = ystart;
t = tstart;

outmat = [t,y]; 	% a place to store results

% the main RK loop

while(t <= tlast)
	
	a = rkf(t,y);
	b = rkf(t+h/2,y+h*a/2);
	c = rkf(t+h/2,y+h*b/2);
	d = rkf(t+h,y+h*c);
	t = t + h;
	y = y + h*(a+2*b+2*c+d)/6;
	
	outmat = [outmat; t,y];	% save results in a matrix
end;

disp(outmat)		% print out the results on the screen

plot(outmat(:,1),outmat(:,2))	% plot a graph of the results
grid;
title('Runge-Kutta method for solving y'' = t - y^2');