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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; /*Time Step*/
n:4/h;
u[0]:1;/*Initial Condition!*/

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

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

h:0.125;
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, [lines,5]]
,[xlabel,"time"]
,[ylabel,"Population"]
,[title,"Numerical Solution to dy/dt=F(t,y)"]
,[legend,"h=0.25","h=0.125","Exact Population"]
)$