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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 149 "LUdec:=proc(a,b,c) \+
local L,U,k,n; n:=nops(b); L:=[b[1]]; U:=[];\nfor k to n-1 do U:=[op(U
),c[k]/L[k]];L:=[op(L),b[k+1]-a[k]*U[k]] end do;\n[a,L,U] end:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "M:=LUdec([-3,1,-2],[3,8,2,6]
,[-3,-2,4]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"MG7%7%!\"$\"\"\"!
\"#7&\"\"$\"\"&#\"#7F,#\"#GF+7%!\"\"#F)F,#F,F+" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 224 "tridset:=proc(M,r) local n,k,a,L,U,y,x; a:=M[
1]; L:=M[2]; U:=M[3]; n:=nops(L);\ny:=[r[1]/L[1]]; for k to n-1 do y:=
[op(y),(r[k+1]-a[k]*y[k])/L[k+1]] end do;\nx:=[y[n]]; for k to n-1 do \+
x:=[y[n-k]-U[n-k]*x[1],op(x)] end do end:" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 22 "tridset(M,[7,8,2,-3]);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#7&#\"$d%\"#%)#\"#()\"#G#\"#:\"#c#!#BF," }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "evalm(matrix(4,4,[3,-3,0,0,-3,8,-2,
0,0,1,2,4,0,0,-2,6])&*%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vector
G6#7&\"\"(\"\")\"\"#!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "
n:=6: A:=0: B:=3:  h:=(B-A)/n:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 17 "p:=z->-exp(z/2.):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
15 "q:=z->ln(1.+z):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "r:=z
->sin(1.*z):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "x:=[seq(A+h
*k,k=1..n-1)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "a:=[seq(1
-h/2*p(x[k]),k=2..n-1)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 
"b:=[seq(-2+h^2*q(x[k]),k=1..n-1)]:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 33 "c:=[seq(1+h/2*p(x[k]),k=1..n-2)]:" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 31 "R:=[seq(h^2*r(x[k]),k=1..n-1)]:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "R[1]:=R[1]-2*(1-h/2*p(x[1])):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "R[n-1]:=R[n-1]+4*(1+h/2*p(x[
n-1])):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "y:=tridset(LUdec
(a,b,c),R);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"yG7'$\"+x/@hA!\"*$
\"+t:N3EF($\"+Z:FJIF($\"+)GF)fMF($\"+IL.]MF(" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 12 "with(plots):" }}{PARA 7 "" 1 "" {TEXT -1 50 "War
ning, the name changecoords has been redefined\n" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 52 "pointplot([[A,2],seq([x[k],y[k]],k=1..n-1),[B
,-4]]);" }}{PARA 13 "" 1 "" {GLPLOT2D 494 494 494 {PLOTDATA 2 "6#-%'PO
INTSG6)7$$\"\"!F($\"\"#F(7$$\"+++++]!#5$\"+x/@hA!\"*7$$\"\"\"F($\"+t:N
3EF17$$\"+++++:F1$\"+Z:FJIF17$F)$\"+)GF)fMF17$$\"+++++DF1$\"+IL.]MF17$
$\"\"$F($!\"%F(" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 
0 0 "Curve 1" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 11 "Richardson:" }{MPLTEXT 1 0 0 "" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "n:=6: A:=1: B:=2:  h:=(B-A)
/n:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "p:=x->-3/(1+x):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "q:=x->4./(1+x)^2:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "r:=x->1.+x:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "x:=[seq(A+h*k,k=1..n-1)]:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "a:=[seq(1-h/2*p(x[k]),k=2..n
-1)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "b:=[seq(-2+h^2*q(x
[k]),k=1..n-1)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "c:=[seq
(1+h/2*p(x[k]),k=1..n-2)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
31 "R:=[seq(h^2*r(x[k]),k=1..n-1)]:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 29 "R[1]:=R[1]-0*(1-h/2*p(x[1])):" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 35 "R[n-1]:=R[n-1]-9*(1+h/2*p(x[n-1])):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "y6:=tridset(LUdec(a,b,c),R);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#y6G7'$\"+t$)>-y!#5$\"+k_86=!\"*
$\"+3cm?JF+$\"+4/sOZF+$\"+$p+so'F+" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 47 "yy6:=[seq(eval(z^3+z^2-z-1.,z=x[k]),k=1..n-1)];" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$yy6G7'$\"*2uS#y!\"*$\"+:[\"[\"=F($
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{MPLTEXT 1 0 7 "y6-yy6;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7'$!)(pv=#!
#5$!(^&zO!\"*$!(#RMVF)$!(K.-%F)$!(ATh#F)" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 31 "n:=12: A:=1: B:=2:  h:=(B-A)/n:" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 25 "x:=[seq(A+h*k,k=1..n-1)]:" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 33 "a:=[seq(1-h/2*p(x[k]),k=2..n-1)]:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "b:=[seq(-2+h^2*q(x[k]),k=1..
n-1)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "c:=[seq(1+h/2*p(x
[k]),k=1..n-2)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "R:=[seq
(h^2*r(x[k]),k=1..n-1)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 
"R[1]:=R[1]-0*(1-h/2*p(x[1])):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 35 "R[n-1]:=R[n-1]-9*(1+h/2*p(x[n-1])):" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 29 "y12:=tridset(LUdec(a,b,c),R);" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#>%$y12G7-$\"+aA)Rh$!#5$\"+n'G'=yF($\"+:3([E\"!\"*$\"+&y
)*Q\"=F-$\"+HLUKCF-$\"+W3#R7$F-$\"+$fn=*QF-$\"+*pR(RZF-$\"+hJ,rcF-$\"+
mQ;*o'F-$\"+)enwz(F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "yy1
2:=[seq(eval(z^3+z^2-z-1.,z=x[k]),k=1..n-1)];" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#>%%yy12G7-$\"*:)*oh$!\"*$\"*2uS#yF($\"++]il7F($\"+:[\"[
\"=F($\"+u!\\MV#F($\"++++DJF($\"+:)RH*QF($\"+T2uSZF($\"++](=n&F($\"+:[
\")*o'F($\"+2C.)z(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "y12-
yy12;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7-$!('*e\"H!#5$!(.aW&F&$!'&=a
(!\"*$!'Ig\"*F+$!(Xd-\"F+$!(c\"z5F+$!(AA2\"F+$!(U5+\"F+$!'R=')F+$!'\\4
lF+$!'>[OF+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "n:=24: A:=1:
 B:=2:  h:=(B-A)/n:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "x:=[
seq(A+h*k,k=1..n-1)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "a:
=[seq(1-h/2*p(x[k]),k=2..n-1)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 34 "b:=[seq(-2+h^2*q(x[k]),k=1..n-1)]:" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 33 "c:=[seq(1+h/2*p(x[k]),k=1..n-2)]:" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 31 "R:=[seq(h^2*r(x[k]),k=1..n-1)]:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "R[1]:=R[1]-0*(1-h/2*p(x[1]))
:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "R[n-1]:=R[n-1]-9*(1+h/
2*p(x[n-1])):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "y24:=trids
et(LUdec(a,b,c),R);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$y24G79$\"+-
\"fkt\"!#5$\"+$**phh$F($\"+bWZVcF($\"+QUrAyF($\"+1J#e,\"!\"*$\"+imVl7F
1$\"+fiaJ:F1$\"+ige9=F1$\"+J-*\\6#F1$\"+DH>LCF1$\"+.$G'pFF1$\"+>0tCJF1
$\"+DP$*)\\$F1$\"+r?n#*QF1$\"+0(zjI%F1$\"+t2\\SZF1$\"+F%Ra>&F1$\"+0)f;
n&F1$\"+WgephF1$\"+'G_'*o'F1$\"+pEHKsF1$\"+D8%zz(F1$\"+!RKqQ)F1" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "yy24:=[seq(eval(z^3+z^2-z-1.
,z=x[k]),k=1..n-1)];" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%%yy24G79$\"*
\\Mot\"!\"*$\"*:)*oh$F($\"*DJXk&F($\"*2uS#yF($\"+!p')f,\"F($\"++]il7F(
$\"+mjvJ:F($\"+:[\"[\"=F($\"+vVB:@F($\"+u!\\MV#F($\"+SH*)pFF($\"++++DJ
F($\"+#G/#*\\$F($\"+:)RH*QF($\"+D1k1VF($\"+T2uSZF($\"+!>uc>&F($\"++](=
n&F($\"+*>x(phF($\"+:[\")*o'F($\"+v=UKsF($\"+2C.)z(F($\"+S/3(Q)F(" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "y24-yy24;" }}{PARA 12 "" 1 "
" {XPPMATH 20 "6#79$!')Qv$!#5$!'d\"G(F&$!(&zc5F&$!(K)f8F&$!'%ej\"!\"*$
!'Q$)=F/$!'2,@F/$!'`(G#F/$!'WTCF/$!'\\hDF/$!'PYEF/$!'\"[p#F/$!'d0FF/$!
'WxEF/$!'?4EF/$!'o*\\#F/$!'jZBF/$!'&>:#F/$!'b6>F/$!'HD;F/$!'1#H\"F/$!&
#3\"*F/$!&]![F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "y6better
:=[seq((4*y12[2*k]-y6[k])/3,k=1..5)];" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#>%)y6betterG7'$\"+Ha5Cy!#5$\"+e*>[\"=!\"*$\"+Bf+DJF+$\"+HhuSZF+$\"+
c#=)*o'F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "y6better-yy6;
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7'$\"&f8$!#5$\"%V^!\"*$\"%BfF)$\"%
)Q&F)$\"%TMF)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "y12better:
=[seq((4*y24[2*k]-y12[k])/3,k=1..11)];" }}{PARA 12 "" 1 "" {XPPMATH 
20 "6#>%*y12betterG7-$\"+S#**oh$!#5$\"+%4wS#yF($\"+y_il7!\"*$\"+b^\"[
\"=F-$\"+d%\\MV#F-$\"+6/+DJF-$\"+I-%H*QF-$\"+J6uSZF-$\"+``(=n&F-$\"+#4
:)*o'F-$\"+rD.)z(F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "y12b
etter-yy12;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7-$\"%!4\"!#5$\"%C?F&$
\"$y#!\"*$\"$S$F+$\"$$QF+$\"$6%F+$\"$:%F+$\"$!RF+$\"$`$F+$\"$x#F+$\"$k
\"F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "y6best:=[seq((16*y1
2better[2*k]-y6better[k])/15,k=1..5)];" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%'y6bestG7'$\"+QT2Cy!#5$\"+N[\"[\"=!\"*$\"+W++DJF+$\"+)zS2u%F+$
\"+\")[\")*o'F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "y6best-y
y6;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7'$\"#o!#5$\"#?!\"*$\"#WF)$\"#d
F)$\"#mF)" }}}}{MARK "23 0 0" 11 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }
{PAGENUMBERS 0 1 2 33 1 1 }