/***********************************************
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Euler.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.
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/* Initializations */


h:0.25;
n:4/h;
y[0]:1;

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

EulerApprox1:create_list([i*h,y[i]],i,0,n);

h:1;
n:4/h;
y[0]:1;

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

EulerApprox2:create_list([i*h,y[i]],i,0,n);

/* Plot the result: */
plot2d(
[
[discrete,EulerApprox1]
,[discrete,EulerApprox2]
,exp(t)
]
,[t,0,4]
,[style
, [points,5,1,10]
, [points,9,1,1]
,[lines,5,1]]
,[xlabel,"x"]
,[ylabel,"y"]
,[legend, false]
)$