{VERSION 3 0 "IBM INTEL NT" "3.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 }{CSTYLE " versuch" 20 256 "Copperplate Gothic Bold" 0 0 255 0 255 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "versuch" -1 257 "Copperplate Gothic Bold" 0 0 255 0 255 1 2 2 2 0 0 2 0 0 0 }{CSTYLE "" 257 258 "Copperplate Gothic Light " 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" 257 259 "Copperplate Gothi c Light" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" 257 260 "Arial Cyr " 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "restart;\n" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "Digits:=20:\n" }{TEXT -1 26 "Differentialgleichung " }{XPPEDIT 18 0 "diff(y,t) = -y;" "6#/-%%d iffG6$%\"yG%\"tG,$F'!\"\"" }{TEXT -1 38 " und ihre exakte L\366sung an der Stelle " }{XPPEDIT 18 0 "t = 1;" "6#/%\"tG\"\"\"" }{TEXT -1 1 ": " }{MPLTEXT 1 0 87 " \n\ndsolve(\{diff(y(t),t)=-y(t),y(0)=1\}, y(t) );\nExakte_lsg:=evalf(subs(t=1,rhs(%)));\n\n" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 46 " Die Startwerte f\374r Aitken-Interpolation " } {XPPEDIT 18 0 "R[0]^i;" "6#)&%\"RG6#\"\"!%\"iG" }{TEXT -1 64 " sind di e numerischen L\366sungen nach der Euler-Methode mit den Sc" }{TEXT 18 0 "" }{TEXT 256 0 "" }{TEXT -1 12 "hrittweiten " }{XPPEDIT 18 0 "h \+ = 1;" "6#/%\"hG\"\"\"" }{TEXT -1 5 " , " }{XPPEDIT 18 0 "1/2;" "6#*& \"\"\"\"\"\"\"\"#!\"\"" }{TEXT -1 5 " , " }{XPPEDIT 18 0 "1/4;" "6#* &\"\"\"\"\"\"\"\"%!\"\"" }{TEXT -1 5 " , " }{XPPEDIT 18 0 "1/8;" "6# *&\"\"\"\"\"\"\"\")!\"\"" }{TEXT -1 5 " , " }{XPPEDIT 18 0 "1/16;" " 6#*&\"\"\"\"\"\"\"#;!\"\"" }{TEXT -1 5 " , " }{XPPEDIT 18 0 "1/32;" "6#*&\"\"\"\"\"\"\"#K!\"\"" }{TEXT -1 5 " , " }{XPPEDIT 18 0 "1/64; " "6#*&\"\"\"\"\"\"\"#k!\"\"" }{TEXT -1 6 " ... " }{XPPEDIT 18 0 "1/( 2^j);" "6#*&\"\"\"\"\"\")\"\"#%\"jG!\"\"" }{TEXT -1 7 " ( " } {XPPEDIT 18 0 "j = 0;" "6#/%\"jG\"\"!" }{TEXT -1 28 " , ... , 9 ) an \+ der Stelle " }{XPPEDIT 18 0 "t = 1;" "6#/%\"tG\"\"\"" }{TEXT -1 2 " : " }{MPLTEXT 1 0 2 "\n\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 193 "for j f rom 0 to 9 do\n g:=dsolve(\{diff(y(t),t)=-y(t),y(0)=1\}, y(t), type=n umeric, method=classical, stepsize=1/(2^j),output=listprocedure );\n gy := subs(g,y(t)):\n R[j,0]:=gy(1);\n od:\n\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 16 " Die Werte " }{XPPEDIT 18 0 "R[m]^i; " "6#)&%\"RG6#%\"mG%\"iG" }{TEXT -1 49 " werden nach dem Dreiecks-Sch ema mit der Formel " }{TEXT 256 3 "(2)" }{TEXT -1 108 " ermittelt: \+ \n \+ " }{TEXT -1 2 " " }{XPPEDIT 18 0 "R[m-1]^(i+1 )+(R[m-1]^(i+1)-R[m-1]^i)/(h[i]/h[i+m]-1);" "6#,&)&%\"RG6#,&%\"mG\"\" \"\"\"\"!\"\",&%\"iGF*\"\"\"F*F**&,&)&F&6#,&F)F*\"\"\"F,,&F.F*\"\"\"F* F*)&F&6#,&F)F*\"\"\"F,F.F,F*,&*&&%\"hG6#F.F*&FA6#,&F.F*F)F*F,F*\"\"\"F ,F,F*" }{TEXT -1 16 " " }{TEXT 258 2 "(2" }{TEXT 260 0 "" }{TEXT 259 1 ")" }{TEXT -1 2 " " }{MPLTEXT 1 0 27 "\n \+ " }{TEXT -1 0 "" }{MPLTEXT 1 0 18 " \n" } }{PARA 0 "> " 0 "" {MPLTEXT 1 0 110 "for m from 1 to 9 do \n for i fr om 0 to 9-m do\n R[i,m]:=R[i+1,m-1]+(R[i+1,m-1] -R[i,m-1])/(2^m-1);\n od;\nod;\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 857 "printf(`Ta belle 2: Die Werte R[m]^i\\n`);\nprintf(`---------------------------- ---------------------------------------------------------------------- -------------------\\n`);\nprintf(` i m | 0 \+ 1 2 3 4 5 \+ 6 \\n`);\nprintf(`------------------------------------------ ---------------------------------------------------------------------- -----\\n`);\nfor i from 0 to 3 do\n printf(` %d | `,i );\n for m from 0 to 6 do\n printf(`%11.9f `, R[i,m]);\n od;\n printf(`\\n`);\nod;\nfor i from 4 to 9 do\n printf(` %d \+ | `,i);\n for m from 0 to 9-i do\n printf(`%11.9f `, R[i,m ]);\n od;\n printf(`\\n`);\nod;\nprintf(`--------------------------- ---------------------------------------------------------------------- --------------------\\n`);\n\n\n\n\n\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 883 "\n\n\n\n\nprintf(`Tabelle 3: Fehler in R[m]^i:\\n`); \nprintf(`------------------------------------------------------------ ---------------------------------------------------------\\n`);\nprint f(` i m | 0 1 2 \+ 3 4 5 6 \\n`);\nprintf(`---- ---------------------------------------------------------------------- -------------------------------------------\\n`);\nfor i from 0 to 3 d o\n printf(` %d | `,i);\n for m from 0 to 6 do\n \+ printf(`%11.9f `, R[i,m]-Exakte_lsg);\n od;\n printf(`\\n`);\nod; \nfor i from 4 to 9 do\n printf(` %d | `,i);\n for m from 0 to 9-i do\n printf(`%11.9f `, R[i,m]-Exakte_lsg);\n od; \n printf(`\\n`);\nod;\nprintf(`------------------------------------- ---------------------------------------------------------------------- ----------\\n`);\n\n\n\n\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 927 "\n\n\n\n\n\n\nprintf(`Tabelle 4: Fehler in R[m]^i / h[i]^(m+1):\\ n`);\nprintf(`-------------------------------------------------------- -------------------------------------------------------------\\n`);\np rintf(` i m | 0 1 2 \+ 3 4 5 6 \\n`);\nprintf(` ---------------------------------------------------------------------- -----------------------------------------------\\n`);\nfor i from 0 to 3 do\n printf(` %d | `,i);\n for m from 0 to 6 do\n printf(`%11.9f `, (R[i,m]-Exakte_lsg)*2^(i*(m+1)));\n od;\n p rintf(`\\n`);\nod;\nfor i from 4 to 9 do\n printf(` %d | \+ `,i);\n for m from 0 to 9-i do\n printf(`%11.9f `, (R[i,m]- Exakte_lsg)*2^(i*(m+1)));\n od;\n printf(`\\n`);\nod;\nprintf(`----- ---------------------------------------------------------------------- ------------------------------------------\\n`);\n\n\n\n\n\n" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "8" 0 }{VIEWOPTS 1 1 0 1 1 1803 }