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;\n#-----------------------------------\nRG4:=proc(x0,xmax,y0,N)\n#---
--------------------------------\n# Negyed rend\373 Runge-Kutta\n# Meg
oldja a dy/dx=f(x,y) differenci\341l egyenletet\n# az [x0,xmax] tartom
\341nyon, N r\351szre osztva azt.\n# A l\351p\351sk\366z h:=(xmax-x0)/
(N-1),\n# az eredm\351ny a result t\341bl\341zat lesz, \n# ami az oszt
\341spontokban sz\341molt \n# x,y \351rt\351kekket tartalmazza  \n#---
--------------------------------\n#  Lok\341lis v\341ltoz\363k\n  loca
l n,h,xval,yval,xx,yy,k1,k2,k3,k4,result::list(numeric);\n#  Glob\341l
is v\341ltoz\363k\n  global f;\n#-------------------------------------
----------------------\n#  RK\n#--------------------------------------
---------------------\n  h:=(xmax-x0)/(N-1);\n  xval:=array(1..N):yval
:=array(1..N):\n  xval[1]:=x0:yval[1]:=y0:\n for n from 1 to N-1 do\n \+
 xx:=xval[n];yy:= yval[n];\n  k1    := f(xx,yy):                  \n  \+
k2    := f(xx+h/2,yy+(h/2)*k1):\n  k3    := f(xx+h/2,yy+(h/2)*k2): \n \+
 k4    := f(xx+h,yy+h*k3):    \n  yval[n+1]:= yy + evalf((h/6.)*(k1+2*
k2+2*k3+k4)):\n  xval[n+1]:=xx+h: \n od:\n result:=[[xval[i],yval[i]] \+
$i=1..N]:\n#----------------------------------------------------------
-\n#  Eredm\351ny\n#--------------------------------------------------
---------\n result\nend;" }{TEXT -1 0 "" }}{PAGEBK }{PARA 12 "" 0 "" 
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316 "#-----------------------------------\n# P\351lda\n#--------------
---------------------\n#dy(x)/dx=f(x,y(x))\n   f:=(x,y) -> 1/y^2;\n#Ke
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" }{TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6$%\"xG%\"y
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{MPLTEXT 1 0 452 "#-----------------------------------\n# Maple megold
\341s, saj\341t megold\341s\n#-----------------------------------\nh:=
(xmax-x0)/(N-1);\nxval:=array(1..N,[Mylist[i][1] $i=1..N]):\nzval:=dso
lve(\{diff(z(t),t)=subs(\{x=t,y=z(t)\},f(x,y)),z(x0)=y0\},numeric,meth
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t], style=[point,line],symbolsize=40,thickness=4,color=[black,blue]);
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#>%%ode1G/-%%diffG6$-%\"zG6#%\"tGF,*&\"\"\"F.*$)F)\"\"#F.!\"\"" }}
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