Implement the Euler scheme for the scalar IVP:  y′(t) = f(t, y(t)),   t0 < t < tend
				        	y(t0) = y0.
The code should read (and print out):  the initial point: t0, y0;   the final time: tend;
and the number of time-steps to be executed: Nsteps.
The evaluation of f(t,y) should be done in a Function Subprogram  FCN( tn, Yn )
which returns the value  Fn = f(tn,Yn).

Calculate the time-step Δt = (tend − t0) / Nsteps,   implement the Euler time-stepping: 
	 Y0 = y0 ;   Yn+1 = Yn + Δt f( tn , Yn ),  for n=0,1,...,Nsteps,  
with timesteps:   tn = t0 + n * Δt ,  n=0,1,...,Nsteps ,
and output the pairs tn, Yn  (and the exact solution when known, see below).
NOTE: No arrays are actually needed...

1. Debug your code on the trivial problem:  y'(t) = 2t,  0 < t < 2,   y(0) = 1,
   by calculating Yexact(tn) = tn*tn + 1, and the error ERRn = ABS(Yexact - Yn).  
   At each step, output  tn, Yn, Yexactn, ERRn, 
   and calculate the worst overall error: ERRmax = MAX( ERRmax, ERRn).  
   Output ERRmax at the end of the run.

Before you type in the code, you should write it on paper, and execute the steps by 
hand/calculator for, say, Nsteps=4, to make sure the logic is right. Then enter the code and
check that it finds the same values. Then try Nsteps=10.

Note that since the RHS of this ODE is just a function of t, the solution is simply the integral 
of  f(t)=2t,  so in fact your code is performing numerical integration (usually called "quadrature").  
What quadrature rule does it amount to ??? (rectange? trapezoidal? Simpson?)

2. Test your code on:  y′(t) = y,  0 < t < 1,  y(0) = 1,   with  Nsteps=10.
   Only need to change the FCN, and the exact solution; comment out previous f and enter this one. 
   Then COMMENT OUT PRINTING of  tn,Yn,...  and try  Nsteps = 100, 1000, 5000, 10000 
   to see how the error decreases.

Here the RHS contains the unknown function y(t) itself, so this is no longer just a quadrature problem!
This example is discussed in the CSEP e-book, chapter: ODE,  2.2.1 Taylor series methods, Euler method (Example 8). 

Submit ONLY the following:
  a. Answer to the question in 1.
  =============================================================
  b. ERRmax for Nsteps= 1000 and 5000   from 2.
  =============================================================
  c. Your code.

You can use gnuplot to plot several curves on the same plot, from columns of a file, as follows: