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demonstrates the use of Maple to i llustrate Gauss-Siedel method, a technique used in solving elliptic pa rtial differential equations." }}}{EXCHG {PARA 210 "" 0 "" {TEXT 208 0 "" }}}{EXCHG {PARA 211 "" 0 "" {TEXT 208 17 "Problem Statement" }}} {EXCHG {PARA 3 "" 0 "" {TEXT 208 246 "Use the direct method to solve f or the temperature distribution of a rectangular plate, rectangular pl ate with a length of 2.4 m and width of 3.0 m. The plate is subjected \+ to dirichlet temperature boundary conditions on the foursides of the p late" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT 213 6 "Inputs" }}{EXCHG {PARA 3 "" 0 "" {TEXT 208 115 "The following simulation approximates the temp erature distribution along the length of the rod. 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\"normal\", fence = \"false\", separator = \" false\", stretchy = \"false\", symmetric = \"false\", largeop = \"fals e\", movablelimits = \"false\", accent = \"false\", lspace = \"0.27777 78em\", rspace = \"0.2777778em\"), Typesetting:-mn(\"0\", bold = \"fal se\", mathvariant = \"normal\"), Typesetting:-mo(\";\", bold = \"false \", mathvariant = \"normal\", fence = \"false\", separator = \"true\", stretchy = \"false\", symmetric = \"false\", largeop = \"false\", mov ablelimits = \"false\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.2777778em\"), Typesetting:-mspace(height = \"0.0ex\", width = \+ \"0.0em\", depth = \"0.0ex\", linebreak = \"newline\"), Typesetting:-m i(\"\1673\", bold = \"false\", italic = \"false\", mathvariant = \"nor mal\"), Typesetting:-mo(\"≔\", bold = \"false\", mathvariant = \"normal\", fence = \"false\", separator = \"false\", stretchy = \"fa lse\", symmetric = \"false\", largeop = \"false\", movablelimits = \"f alse\", accent = \"false\", lspace = 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\"normal\", fence = \"false\", separator = \"true\", stretchy = \"false\", symmetric = \"false\", la rgeop = \"false\", movablelimits = \"false\", accent = \"false\", lspa ce = \"0.0em\", rspace = \"0.2777778em\"), Typesetting:-mo(\" \", bold = \"false\", mathvariant = \"normal\", fence = \"false\", separator = \"false\", stretchy = \"false\", symmetric = \"false\", largeop = \"f alse\", movablelimits = \"false\", accent = \"false\", lspace = \"0.0e m\", rspace = \"0.0em\"), Typesetting:-mspace(height = \"0.0ex\", widt h = \"0.0em\", depth = \"0.0ex\", linebreak = \"newline\"), Typesettin g:-mi(\"tol\", bold = \"false\", italic = \"true\", mathvariant = \"it alic\"), Typesetting:-mo(\"≔\", bold = \"false\", mathvariant \+ = \"normal\", fence = \"false\", separator = \"false\", stretchy = \"f alse\", symmetric = \"false\", largeop = \"false\", movablelimits = \" false\", accent = \"false\", lspace = \"0.2777778em\", rspace = \"0.27 77778em\"), Typesetting:-mn(\"1.0\", bold = \"false\", mathvariant = \+ \"normal\"), Typesetting:-mo(\";\", bold = \"false\", mathvariant = \" normal\", fence = \"false\", separator = \"true\", stretchy = \"false \", symmetric = \"false\", largeop = \"false\", movablelimits = \"fals e\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.2777778em\") );" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6\\o-I#miGF$ 6&Q(restartF'/%%boldGQ&falseF'/%'italicGQ%trueF'/%,mathvariantGQ'itali cF'-I#moGF$6.Q\";F'F//F6Q'normalF'/%&fenceGF1/%*separatorGF4/%)stretch yGF1/%*symmetricGF1/%(largeopGF1/%.movablelimitsGF1/%'accentGF1/%'lspa ceGQ&0.0emF'/%'rspaceGQ,0.2777778emF'-I'mspaceGF$6&/%'heightGQ&0.0exF' /%&widthGFN/%&depthGFW/%*linebreakGQ(newlineF'-FS6&FUFXFZ/FgnQ%autoF'- F,6&Q%withF'F/F2F5-I(mfencedGF$6%-F#6#-F,6&Q'linalgF'F/F2F5F/F<-F96.Q \":F'F/F/FAF1FBFDFFFHFJ/FMFQFO-F96.Q\"~F'F/FF[pFBFDFFFHFJFL/FPFN FRF]o-Fao6%-F#6#-F,6&Q.LinearAlgebraF'F/F2F5F/FF[pFBFDFFFHFJF\\pFO-I#mnGF$6%Q$2.4F'F/F " 0 "" {XPPEDIT 0 1 "`assign`(dy, dx);" "-I%mrowG6#/I+modulenameG6\" I,TypesettingGI(_syslibGF'64-I#miGF$6&Q#dyF'/%%boldGQ&falseF'/%'italic GQ%trueF'/%,mathvariantGQ'italicF'-I#moGF$6.Q*≔F'F//F6Q'normal F'/%&fenceGF1/%*separatorGF1/%)stretchyGF1/%*symmetricGF1/%(largeopGF1 /%.movablelimitsGF1/%'accentGF1/%'lspaceGQ,0.2777778emF'/%'rspaceGFN-F ,6&Q#dxF'F/F2F5-F96.Q\";F'F/F/FAF4FBFDFFFHFJ/FMQ&0.0emF'FO-I'mspace GF$6&/%'heightGQ&0.0exF'/%&widthGFY/%&depthGFin/%*linebreakGQ(newlineF '-F96.Q\"~F'F/FF@FBFDFFFHFJFX/FPFY-F,6&Q\"mF'F/F2F5F8-F,6&Q&roundF' F//F3F1F<-I(mfencedGF$6%-F#6#-I&mfracGF$6(-F,6&Q\"lF'F/F2F5-F#6#FQ/%.l inethicknessGQ\"1F'/%+denomalignGQ'centerF'/%)numalignGF^q/%)bevelledG F1F/F " 0 "" {XPPEDIT 19 1 "`assign`(T, matrix(`+`(n, 1 ), `+`(m, 1))); -1; print(T);" "-I%mrowG6#/I+modulenameG6\"I,Typesetti ngGI(_syslibGF'6+-I#miGF$6(Q\"TF'/%'familyGQ,Courier~NewF'/%'italicGQ% trueF'/%+foregroundGQ*[255,0,0]F'/%0font_style_nameGQ,Maple~InputF'/%, mathvariantGQ'italicF'-I#moGF$60Q*≔F'F/F5F8/F " 0 "" {XPPEDIT 19 1 "for i to `+`(n, 1) do for j to `+`(m, 1) do `assign`(T[ i, j], Ti) end do end do:" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI (_syslibGF'6fo-I#moGF$62Q$forF'/%'familyGQ,Courier~NewF'/%%boldGQ%true F'/%+foregroundGQ*[255,0,0]F'/%0font_style_nameGQ,Maple~InputF'/%,math variantGQ%boldF'/%+fontweightGF=/%&fenceGQ&falseF'/%*separatorGFB/%)st retchyGFB/%*symmetricGFB/%(largeopGFB/%.movablelimitsGFB/%'accentGFB/% 'lspaceGQ&0.0emF'/%'rspaceGFQ-F,60Q\"~F'F/F5F8/FF@FCFEFGFIFKFMFOFRFT-I#mnGF$6'Q\"1F'F/F5F8FWFT-F,62Q#byF'F/ F2F5F8F;F>F@FCFEFGFIFKFMFOFRFTF^oFT-F,62Q#toF'F/F2F5F8F;F>F@FCFEFGFIFK FMFOFRFT-FZ6(Q\"nF'F/FgnF5F8Fin-F,60Q\"+F'F/F5F8FWF@FCFEFGFIFKFM/FPQ,0 .2222222emF'/FSF_pF^oFT-F,62Q#doF'F/F2F5F8F;F>F@FCFEFGFIFKFMFOFR-I'msp aceGF$6&/%'heightGQ&0.0exF'/%&widthGFQ/%&depthGFip/%*linebreakGQ(newli neF'FTFTFTFTF+FT-FZ6(Q\"jF'F/FgnF5F8FinFTF[oFTF^oFTFboFTF^oFTFeoFT-FZ6 (Q\"mF'F/FgnF5F8FinF[pF^oFTFapFTFTFdpFTFTFTFTFTFTFT-FZ6(Q\"TF'F/FgnF5F 8Fin-I(mfencedGF$6+-F#6%FY-F,60Q\",F'F/F5F8FWF@/FDF4FEFGFIFKFMFO/FSQ,0 .3333333emF'FaqF/F2F5F8F;F>/%%openGQ\"[F'/%&closeGQ\"]F'-F,60Q*&colone q;F'F/F5F8FWF@FCFEFGFIFKFM/FPQ,0.2777778emF'/FSF_s-FZ6(Q#TiF'F/FgnF5F8 Fin-F,60Q\";F'F/F5F8FWF@FbrFEFGFIFKFMFOF`sFdp-Fep6&FgpFjpF\\q/F_qQ%aut oF'FdpFTFTFTFT-F,62Q$endF'F/F2F5F8F;F>F@FCFEFGFIFKFMFOFRFTFap-F,60Q\": F'F/F5F8FWF@FCFEFGFIFKFMF^sF`sFdpF[tFTFapF^t" }}}{EXCHG {PARA 0 "" 0 " " {TEXT 208 50 "The following loop assigns the boundary conditions" }} }{EXCHG {PARA 0 "> " 0 "" {TEXT 214 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "for i to `+`(n, 1) do for j to `+`(m, 1) do if i = 1 th en `assign`(T[i, j], TB) end if; if i = `+`(n, 1) then `assign`(T[i, j ], TU) end if; if j = 1 then `assign`(T[i, j], TL) end if; if j = `+`( m, 1) then `assign`(T[i, j], TR) end if end do end do; -1; `assign`(it eration, 0); 1; print(T);" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI (_syslibGF'6jx-I#moGF$62Q$forF'/%'familyGQ,Courier~NewF'/%%boldGQ%true F'/%+foregroundGQ*[255,0,0]F'/%0font_style_nameGQ,Maple~InputF'/%,math variantGQ%boldF'/%+fontweightGF=/%&fenceGQ&falseF'/%*separatorGFB/%)st retchyGFB/%*symmetricGFB/%(largeopGFB/%.movablelimitsGFB/%'accentGFB/% 'lspaceGQ&0.0emF'/%'rspaceGFQ-F,60Q\"~F'F/F5F8/FF@FCFEFGFIFKFMFOFRFT-I#mnGF$6'Q\"1F'F/F5F8FWFT-F,62Q#byF'F/ F2F5F8F;F>F@FCFEFGFIFKFMFOFRFTF^oFT-F,62Q#toF'F/F2F5F8F;F>F@FCFEFGFIFK FMFOFRFT-FZ6(Q\"nF'F/FgnF5F8Fin-F,60Q\"+F'F/F5F8FWF@FCFEFGFIFKFM/FPQ,0 .2222222emF'/FSF_pF^oFT-F,62Q#doF'F/F2F5F8F;F>F@FCFEFGFIFKFMFOFR-I'msp aceGF$6&/%'heightGQ&0.0exF'/%&widthGFQ/%&depthGFip/%*linebreakGQ(newli neF'FTFTFTFTF+FT-FZ6(Q\"jF'F/FgnF5F8FinFTF[oFTF^oFTFboFTF^oFTFeoFT-FZ6 (Q\"mF'F/FgnF5F8FinF[pF^oFTFapFTFTFdpFTFTFTFTFTFTFdpFTFTFTFTFTFT-F,62Q #ifF'F/F2F5F8F;F>F@FCFEFGFIFKFMFOFRFT-I(mfencedGF$6'-F#6%FY-F,60Q\"=F' F/F5F8FWF@FCFEFGFIFKFM/FPQ,0.2777778emF'/FSFcrF^oF/F5F8FWFT-F,62Q%then F'F/F2F5F8F;F>F@FCFEFGFIFKFMFOFRFdpFTFTFTFTFTFTFT-FZ6(Q\"TF'F/FgnF5F8F in-F[r6)-F#6%FY-F,60Q\",F'F/F5F8FWF@/FDF4FEFGFIFKFMFO/FSQ,0.3333333emF 'FaqF/F5F8FW/%%openGQ\"[F'/%&closeGQ\"]F'-F,60Q*≔F'F/F5F8FWF@F CFEFGFIFKFMFbrFdr-FZ6(Q#TBF'F/FgnF5F8Fin-F,60Q\";F'F/F5F8FWF@FbsFEFGFI FKFMFOFdrFdpFTFTFTFTFTFT-F,62Q$endF'F/F2F5F8F;F>F@FCFEFGFIFKFMFOFRFTFg q-F,60Q\":F'F/F5F8FWF@FCFEFGFIFKFMFbrFdrFdpFTFTFdpFTFTFTFTFTFgqFT-F[r6 '-F#6'FYF_rFhoF[pF^oF/F5F8FWFTFerFdpFTFTFTFTFTFTFTFhrF[sF[t-FZ6(Q#TUF' F/FgnF5F8FinFatFdpFTFTFTFTFTFdtFTFgqFgtFdpFTFdpFTFTFTFTFTFgqFT-F[r6'-F #6%FaqF_rF^oF/F5F8FWFTFerFdpFTFTFTFTFTFTFTFhrF[sF[t-FZ6(Q#TLF'F/FgnF5F 8FinFatFdpFTFTFTFTFTFdtFTFgqFgtFdpFTFdpFTFTFTFTFgqFT-F[r6'-F#6'FaqF_rF dqF[pF^oF/F5F8FWFTFerFdpFTFTFTFTFTFTFTFhrF[sF[t-FZ6(Q#TRF'F/FgnF5F8Fin FatFdpFTFTFTFTFTFdtFTFgqFgtFdp-Fep6&FgpFjpF\\q/F_qQ%autoF'FdpF_vFdpFTF TFTFTFdtFTFapFgtFdpFdtFTFapFgtFdp-FZ6(Q*iterationF'F/FgnF5F8FinF[t-F_o 6'Q\"0F'F/F5F8FWFatFdp-FZ6(Q&printF'F/FgnF5F8Fin-F[r6'-F#6#FhrF/F5F8FW " }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "I\"TG6\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 208 74 "Solving for temp eraturatures after each iteration using Gauss-Sidel Method" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 0 1 "`assign`(count, `*`(`+`(m, `-`(1)), `* `(`+`(n, `-`(1))))):" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_sys libGF'6`al-I#miGF$6&Q&countF'/%%boldGQ&falseF'/%'italicGQ%trueF'/%,mat hvariantGQ'italicF'-I#moGF$6.Q*≔F'F//F6Q'normalF'/%&fenceGF1/% *separatorGF1/%)stretchyGF1/%*symmetricGF1/%(largeopGF1/%.movablelimit sGF1/%'accentGF1/%'lspaceGQ,0.2777778emF'/%'rspaceGFN-I(mfencedGF$6%-F #6%-F,6&Q\"mF'F/F2F5-F96.Q(−F'F/FF@FBFDFFFHFJ/FMQ,0.2222222em F'/FPFgn-I#mnGF$6%Q\"1F'F/FF@FBFDFFFHFJ/FMQ& 0.0emF'/FPFao-FR6%-F#6%-F,6&Q\"nF'F/F2F5FYFinF/F<-F96.Q\":F'F/FF@FB FDFFFHFJFLFO-I'mspaceGF$6&/%'heightGQ&0.0exF'/%&widthGFao/%&depthGFbp/ %*linebreakGQ(newlineF'-F96.Q\"~F'F/FF@FBFDFFFHFJF`oFboFjpFjp-F96.Q &whileF'/F6Q%boldF'/%+fontweightGFaqF>F@FBFDFFFHFJF`oFboFjp-FR6%-F#6%F +-F96.Q\">F'F/FF@FBFDFFFHFJFLFO-Fjn6%Q\"0F'F/FF@FBFDFFFHFJF`oFboF]pFjpFjpFjpFjpFjpFjpFjpF+F8F[rFjoF]pF]pFjpFjp FjpFjpFjp-F96.Q$forF'F`qFbqF>F@FBFDFFFHFJF`oFboFjp-F,6&Q\"iF'F/F2F5Fjp -F96.Q%fromF'F`qFbqF>F@FBFDFFFHFJF`oFboFjp-Fjn6%Q\"2F'F/FF@FBFDFFFHFJF`oFboFjpFinFjp-F96.Q#toF'F`qFbqF>F@FBFDFFFHFJF` oFboFjpFgoFjpF^rF]pFjpFjpFjpFjpFjpFjpFjpFjpFarFjp-F,6&Q\"jF'F/F2F5FjpF grFjpFjrFjpF]sFjpFinFjpF`sFjpFVFjpF^rF]pFjpFjpFjpFjpFjpFjpFjpFjpFjpFjp FjpFjp-F,6&Q$oldF'F/F2F5F8-F,6&Q\"TF'F/F2F5-FR6'-F#6%Fdr-F96.Q\",F'F/F /FAF4FBFDFFFHFJF`o/FPQ,0.3333333emF'FcsF/FFctFBFDFFFHFJF`oFOF]pFjpFjpFjpFjpFjpFjpFjpFjpFjp FjpFjpFjpFisF\\tF8-I&mfracGF$6(-F#6.Fis-FR6'-F#6'Fdr-F96.Q\"+F'F/FF @FBFDFFFHFJFfnFhnFinF`tFcsF/FF@FBFDFFFHFJF`oFboFjp-FR6%-F#6%FhxFhq-F,6&Q$tolF'F/F2F5F/FF@FBFDFFFHFJF`oFboF]pFjpFjpFjpFjpFjpFjpFjpFjpFjpFjpF jpFjpFjpFjpF+F8F+FhuFinFjoF]pFjpFjpFjpFjpFjpFjpFjpFjpFjpFjpFjp-F96.Q$e ndF'F`qFbqF>F@FBFDFFFHFJF`oFboFjpF[zF]pFjpFjpFjpFjpFjpFjpFjpFjpFjpFjpF jpFjpF]p-F^p6&F`pFcpFep/FhpQ%autoF'F]pFjpFjpFjpFjpFjpFjpFhzFjpF^rFjoF] pFjpFjpFjpFjpFjpFjpFjpFjpFjpFhzFjpF^rFjoF]pFjp-F,6&Q*iterationF'F/F2F5 F8F_[lFhuFinF\\uF]pF]pFjp-F,6&Q)TdisplayF'F/F2F5F8-F,6&Q'matrixF'F/F2F 5-FR6%-F#6)FgoFhuFinF`tFVFhuFinF/F " 0 "" {TEXT 214 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "`?`;" }}{PARA 11 "" 1 "" {XPPMATH 20 "I\"?G6\"" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "" "%#%?G" }}}} {MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }