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{SECT 0 {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 256 65 "Multi-D Euler's m
ethod: Lorenz model, a system of 3 nonlinear DEs" }}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 553 "restart:\nf:=10*(y-x);\ng:=28*x-y-x*z;\nh:=-8
*z/3+x*y;\n\n\ndt:=0.01:\ntmax:=50.0:\nn:=ceil(tmax/dt):  \nt:=0.0:  \+
\nx:=1.0:  \ny:=1.0:\nz:=1.0:  \ntxdata[0] := [t,x]:  \nxyzdata[0] := \+
[x,y,z]:  \nfor i from 1 to n do     \n   mk := f:     \n   nk := g:\n
   ok := h;     \n   x := x + dt*mk:     \n   y := y + dt*nk:\n   z :=
 z + dt*ok:     \n   t := t + dt:     \n   txdata[i] := [t,x]:   \n   \+
xyzdata[i] := [x,y,z]:  \nod:  \nt:='t': x:='x': y:='y': z:='z':      \+
          # (clean-up)\ntxdatalist := [ seq( txdata[i], i=0..n ) ]:  \+
\nxyzdatalist := [ seq( xyzdata[i], i=0..n ) ]:\n" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"fG,&%\"yG\"#5*&F'\"\"\"%\"xGF)!\"\"" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%\"gG,(%\"xG\"#G%\"yG!\"\"*&F&\"\"\"%\"zGF+F)" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"hG,&%\"zG#!\")\"\"$*&%\"xG\"\"\"%
\"yGF,F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 350 "equilibria:=[[
0,0,0],[sqrt(72),sqrt(72),27],\n                     [-sqrt(72),-sqrt(
72),27]]:\np_eq:=plots[pointplot3d](equilibria,style=point,color=red,
\n                         symbol=circle):\np_sol:=plots[pointplot3d](
xyzdatalist,style=line,color=black,\n                      axes=normal
,color=blue):\nplots[display](p_sol,p_eq,labels=['x','y','z']);" }}
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