/***********************************************
************************************************
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Stiff.mac

This software is a part of:
Kai Velten: Mathematical Modeling and Simulation, Wiley-VCH, 2009.

It can be used under the conditions of the GNU General Public License (GPLv3),
see http://www.gnu.org/licenses/gpl.html.
************************************************
************************************************
************************************************/

/* Initializations */


h:0.125;
/* h:0.25; */
n:1/h;
y[0]:1;

for i:1 thru n step 1 do
   y[i]:(1-15*h)*y[i-1];

EulerApprox:create_list([i*h,y[i]],i,0,n);


eq:'diff(y,t) = -15*y$  

/* Solve ODE: */
 sol: rk(rhs(eq),y,1,[t,0,1,h])$
/*RK4Approx:create_list([i*h , soln[i]],i,0,n);
*/


/* Plot the result: */
plot2d(
[
[discrete,EulerApprox],
[discrete,sol],
exp(-15*t)
]
,[t,0,1]
,[xlabel,"x"]
,[ylabel,"y"]
,[legend, "EulerApprox", "RK" ," Exact"]
)$