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yD!\"*$\"+\"f4N!**!#57$$\"+05M$f#!\"*$\"+Yix<**!#57$$\"+:no3E!\"*$\"+>
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\"+z.v_E!\"*$\"+$H`w&**!#57$$\"+@?roE!\"*$\"+c\"**['**!#57$$\"+yuz#o#!
\"*$\"+FpNq**!#57$$\"+r\"\\!*p#!\"*$\"+udqv**!#57$$\"+s]r8F!\"*$\"+bYx
z**!#57$$\"+9iAGF!\"*$\"+y))=$)**!#57$$\"+`.$Qu#!\"*$\"*aui)**!\"*7$$
\"+9w\\fF!\"*$\"+B)\\)))**!#57$$\"+.DvtF!\"*$\"+cY!3***!#57$$\"*c!*))y
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^***!#57$$\"+'3NN$G!\"*$\"+'pgg***!#57$$\"+C-X\\G!\"*$\"+)y!*o***!#57$
$\"+\"H6W'G!\"*$\"+.;_(***!#57$$\"*&yAzG!\")$\"+N$G!)***!#57$$\"+'>cS*
G!\"*$\"+>$Q%)***!#57$$\"*<!=4H!\")$\"*<u()***!\"*7$$\"+H8@DH!\"*$\"+#
Hc!****!#57$$\"+K.\"*RH!\"*$\"+P3E****!#57$$\"+N,UaH!\"*$\"1,++'o@%***
*!#;7$$\"+x3$*pH!\"*$\"+Bsb****!#57$$\"+^yS&)H!\"*$\"+jCm****!#57$$\"#
I!\"\"$\"+a)R(****!#5-%&COLORG6'%$RGBG$\")C)eq%!\")$\"\"!!\"\"$\"('>!
\\&!\")-%+_ATTRIBUTEG6#/%'sourceG%,mathdefaultG-%%VIEWG6$;$\"\"!!\"\"$
\"#I!\"\"%(DEFAULTG-&%&_AXISG6#\"\"\"6&-%&COLORG6&%$RGBG$\"\"!!\"\"$\"
\"!!\"\"$\"\"!!\"\"-%*LINESTYLEG6#\"\"!-%*THICKNESSG6#\"\"!-%-TRANSPAR
ENCYG6#$\"\"!!\"\"-&%&_AXISG6#\"\"#6&-%&COLORG6&%$RGBG$\"\"!!\"\"$\"\"
!!\"\"$\"\"!!\"\"-%*LINESTYLEG6#\"\"!-%*THICKNESSG6#\"\"!-%-TRANSPAREN
CYG6#$\"\"!!\"\"-%+AXESLABELSG6$Q!6\"Q!6\"-%)_VISIBLEG6#\"\"\"-%%ROOTG
6'-%)BOUNDS_XG6#$\"$g'!\"\"-%)BOUNDS_YG6#$\"$S\"!\"\"-%-BOUNDS_WIDTHG6
#$\"%+z!\"\"-%.BOUNDS_HEIGHTG6#$\"%!*\\!\"\"-%)CHILDRENG6\"-%+ANNOTATI
ONG6'-%)BOUNDS_XG6#$\"\"!!\"\"-%)BOUNDS_YG6#$\"\"!!\"\"-%-BOUNDS_WIDTH
G6#$\"%+S!\"\"-%.BOUNDS_HEIGHTG6#$\"%+S!\"\"-%)CHILDRENG6\"" 1 2 2 1 
10 0 2 0 0 4 2 1.0 45.0 45.0 0 0 "Curve 1" }}{TEXT 220 0 "" }}}{EXCHG 
{PARA 208 "" 0 "" {TEXT 211 36 "create arrays for numerical solution" 
}}{PARA 208 "> " 0 "" {MPLTEXT 1 210 8 "N := 25;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ">I\"NG6\"\"#D" }}}{EXCHG {PARA 208 "> " 0 "" {MPLTEXT 1 
210 19 "h := (x1-x0)/(N-1);" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I\"hG6\"
#\"\"\"\"\")" }}}{EXCHG {PARA 208 "> " 0 "" {MPLTEXT 1 210 20 "for i f
rom 1 to N do" }{MPLTEXT 1 210 1 "\n" }{MPLTEXT 1 210 19 "  xx[i] := (
i-1)*h:" }{MPLTEXT 1 210 1 "\n" }{MPLTEXT 1 210 7 "end do:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "sol1 := dsolve(\{ode,ic\},y(x),nume
ric,method=classical[foreuler],stepsize=h);\n" }{MPLTEXT 1 0 72 "sol2 \+
:= dsolve(\{ode,ic\},y(x),numeric,method=classical[rk2],stepsize=h);\n
" }{MPLTEXT 1 0 72 "sol3 := dsolve(\{ode,ic\},y(x),numeric,method=clas
sical[rk4],stepsize=h);\n" }{MPLTEXT 1 0 21 "for i from 1 to N do\n" }
{MPLTEXT 1 0 25 "  yy1[i] := sol1(xx[i]):\n" }{MPLTEXT 1 0 25 "  yy2[i
] := sol2(xx[i]):\n" }{MPLTEXT 1 0 25 "  yy3[i] := sol3(xx[i]):\n" }
{MPLTEXT 1 0 31 "  yyy1[i] := op([2,2],yy1[i]):\n" }{MPLTEXT 1 0 31 " \+
 yyy2[i] := op([2,2],yy2[i]):\n" }{MPLTEXT 1 0 31 "  yyy3[i] := op([2,
2],yy3[i]):\n" }{MPLTEXT 1 0 8 "end do:\n" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ">I%sol1G6\"f*6#I,x_classicalGF$6+I%_resGF$I%_datGF$I&_var
sGF$I*_solnprocGF$I&_xoutGF$I'_ndsolGF$I&_parsGF$I#_nGF$I#_iGF$6#IinCo
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\"\"\"9#YQBinvalid~input:~too~many~argumentsF$>I8_EnvDSNumericSaveDigi
tsGF$I'DigitsGF$>F=\"#:@%/I-_EnvInFsolveGF$I%trueG%*protectedG>8(-&I&e
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GF$61F-F0I$_y0GF$I$_ynGF$I$_ylGF$I%_ctlGF$I&_octlGF$I(_reinitGF$I'_err
cdGF$I%_fcnGF$F1I&_yiniGF$F/I%_iniGF$I%_parGF$6#IaoCopyright~(c)~2002~
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$I&falseGFDC1>8$FL>8)X*FRF$F$[gl!!%!!!\"*\"*F7$\"\"!FhoFgo$\"0++++++D
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[gl!!%!!!\"\"\"\"Fho>8-f*6&I\"NG6#/I'_localGFDI1_n47224189879104GF$I\"
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7F`s\"\"#,&F7F7&9&FepFjpF7FhoF$F$F$>807\"@$4-I%typeGFD6$Fco.I(numericG
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20 ">I%sol2G6\"f*6#I,x_classicalGF$6+I%_resGF$I%_datGF$I&_varsGF$I*_so
lnprocGF$I&_xoutGF$I'_ndsolGF$I&_parsGF$I#_nGF$I#_iGF$6#IinCopyright~(
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