{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Warning" -1 7 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 1 1 3 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple P lot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {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 0 224 "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]]; f or 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 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 20 "y''.y=(y')^2/(1+x)^2" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "n:=6: A:=0: B:=2: h:=(B-A)/evalf(n): \+ y[0]:=sqrt(2.): y[n]:=sqrt(10.):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "x:=[seq(A+h*i,i=1..n-1)]:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 86 "F:=[seq((y[i+1]-2*y[i]+y[i-1])/h^2*y[i]-((y[i+1]-y[ i-1])/2/h)^2/(1+x[i])^2,i=1..n-1)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "a:=[seq(diff(F[i],y[i-1]),i=2..n-1)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "b:=[seq(diff(F[i],y[i]),i=1..n-1)]: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "c:=[seq(diff(F[i-1],y[i ]),i=2..n-1)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "y:=[seq(y [0]+(y[n]-y[0])*i/evalf(n),i=1..n-1)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "for k to 4 do y:=y-tridset(LUdec(a,b,c),F) end do;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"yG7'$\"+Z:ro;!\"*$\"+XgMY>F($\"+ .7hQAF($\"+Xa^SDF($\"+-*Q!\\GF(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% \"yG7'$\"+9F($\"+h]RPAF($\"+)*>fRDF($\"+W@a[GF(" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"yG7'$\"+*3hxm\"!\"*$\"+p12X>F($\"+ %H%RPAF($\"+H9fRDF($\"+V=a[GF(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\" yG7'$\"+*3hxm\"!\"*$\"+p12X>F($\"+%H%RPAF($\"+H9fRDF($\"+V=a[GF(" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has been redefined\n " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "pointplot([[A,sqrt(2)], seq([x[i],y[i]],i=1..n-1),[B,sqrt(10)]]);" }}{PARA 13 "" 1 "" {GLPLOT2D 496 496 496 {PLOTDATA 2 "6#-%'POINTSG6)7$$\"\"!F($\"+iN@99! 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