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{SECT 0 {SECT 0 {PARA 20 "" 0 "" {TEXT -1 51 "Euler's method for a 2D \+
system implemented in Maple" }}{PARA 0 "" 0 "" {TEXT -1 96 "Below, eve
rything after a # on a line is just a comment and is ignored by the Ma
ple interpreter." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1760 "restar
t:\ny:=1:         # This is the initial value of y\nv:=1:            #
 This is the initial value of v\nt:=0.0:          # This is the initia
l time\ntF:=20.0:         # This is the value of t we want to get to.
\nn:=300;          # Here we say how many steps we want to take.\nh:=(
tF-t)/n;     # This is our step-size.\n\ndata[0]:=[t,y,v]:  # We store
 the initial point so we can\n                 # plot it later.\nfor i
 from 1 to n do    # This is how to make a block of\n                 \+
       # code get executed n times.\n   mk := v:             # The RHS
 of the first DE\n   nk := -y+(1-y^2)*v:  # The RHS of the second DE\n
   y := y + h*mk:       # The Euler-method steps\n   v := v + h*nk:\n \+
  t := t + h:\n   data[i] := [t,y,v]:  # Store the current point so we
 can\n                      # plot it later.\nod:              # This \+
(\"do\" backwards) marks the end\n                 # of the \"do\" blo
ck.\nh,t,y,v;           # For reference, write out the stepsize and \n
                 # final t, y, and v values.\nunassign('t','y','v','h'
):  # Clean up\n  \ndatalist := [ seq( data[i], i=0..n ) ]:\n         \+
        # This puts all the data into a list\n                 # suita
ble for plotting.\n                 # If you don't want to see this bi
g list, \n                 # change the semicolon to a colon.\nplots[p
ointplot3d]( datalist, labels=[\"t\",\"x\",\"y\"],style=POINT, color=b
lack,axes=BOXED);\n                 # This plots the (approximation to
 the)\n                 # solution in the phase plane.\n              \+
   # The POINT style means each\n                 # data point is mark
ed with a symbol of\n                 # some kind. If \"style=POINT\" \+
were omitted,\n                 # the data points would be joined with
\n                 # straight line segments (try it!)." }}{PARA 0 "" 
0 "" {TEXT -1 113 "Remember that you must ensure the step size is smal
l enough by repeatedly doubling the number of steps  until the" }}
{PARA 0 "" 0 "" {TEXT -1 35 "results don't change significantly." }}
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