%Script that demonstrates the Runge-Kutta integration for a first order problem using Matlab.

% The problem to be solved is:

%y'(t)+2*y(t)=3*exp(-4*t)

%Note: this problem has a known exact solution
% y(t)=2.5*exp(-2*t)-1.5*exp(-4*t)

h=0.1;		%h is the time step.
t=0:h:4;	%initialize time variable.


yPrimeStar(1)=1.0;	%initial condition (same for approximation).

for i=1:length(t)-1,	%Set up "for" loop.
   k1=3*exp(-4*t(i))-2*yPrimeStar(i);	%Calculate derivative;
   ystar=yPrimeStar(i)+h*k1;				%Estimate new value of y*(to+h).
   k2=3*exp(-4*(t(i)+h))-2*ystar;		%Calculate derivative at end of step.
   yPrimeStar(i+1)=yPrimeStar(i)+h*(k1+k2)/2;		%Estimate new value of y'*(to+h).
end