This section contains listing of the Maple worksheet corresponding to the Radioactive Decay examples. These are given in case direct download of the worksheet in either the MAC or PC version gave you difficulties on your computer.
restart:
NO := 1000:
# initial number
of nuclei
k := 10:
# decay constant
start := 0:
# initial time
dt := 0.02:
# time step
N_time := 10: # No of time steps
exact := t -> NO*exp(-k*t):
# exact solution
# Euler method
tt[1] := start:
NN[1] := NO:
for i from 2 to N_time
do
tt[i] := tt[i-1] + dt
rhs_N := - k*NN[i-1];
NN[i] := NN[i-1] +
rhs_N*dt;
od:
# plot the results
with(plots):
plot_1 := plot ( [ [tt[n],NN[n]] $n=1..N_time ] , t=0..(N_time-1)*dt,
style=POINT ):
plot_2 := plot ( exact(t) , t=0..(N_time-1)*dt ):
display( {plot_1, plot_2});
restart:
NO := 1000:
# initial number of nuclei
k := 10:
# decay constant
start := 0:
# initial time
dt := 0.02:
# time step
N_time := 10:
# No of time steps
exact := t -> NO*exp(-k*t):
# exact solution
# Euler and Mid-Point Methods
dt2 := 0.5*dt:
tt[1] := start:
NN_mid[1] := NO:
NN_euler[1] := NO:
for i from 2 to N_time
do
tt[i] := tt[i-1] + dt;
rhs_N := -
k*NN_euler[i-1];
NN_euler[i] :=
NN_euler[i-1] + rhs_N*dt;
rhs_N := - k*NN_mid[i-1];
NN_half := NN_mid[i-1]
+ rhs_N*dt2;
rhs_N := - k*NN_half;
NN_mid[i] := NN_mid[i-1] + rhs_N*dt;
od:
# plot results
with(plots):
plot_1 := plot ( [ [tt[n],NN_euler[n]] $n=1..N_time ] , style=POINT,
symbol=CROSS ):
plot_2 := plot ( exact(t) , t=0..(N_time-1)*dt ):
plot_3 := plot ( [ [tt[n],NN_mid[n]] $n=1..N_time ] ,
style=POINT ):
display( {plot_1, plot_2, plot_3}, title=`Radioactive Decay`);
Exercises
Chapter 8
TOC
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