RrIO*b[-N7*Ur".i5?ZI6c7OM!69Y:Va'Cna#fGC^&C=7Am11(^\)RP016fCg@$cT3OA\UlW[+Mp3rb!9DaKD$\m%Q/sg2X(2mR^^kCP=2@FhN2$P=/5p1bbb=:Fa << "ga"fp1+8>;:_l/iH&:d;H= Mnrl0-qWJj%6TGlA]pn?EX=OUV]^b9?pk\gDo'aMe`u]^:Ob-+h.Zb\cO8hp:(Y=`(E.)SMP6 b1[q0i/G5,SHu66G9oSjR;UcWeWQ"!p.q.hcn`N;Wd((YN6*7&>S4u9m0\X0c>V*8fQVrTi3"WoN`Yu13pa0_h],ZnVlZDj2>ird(rA!el@Ai İ% [›¡Ää/2ü Ğ'ʽê6 q?=L`'Y#.*`]691`moip0kXG,2Ms:"G-H8j:U^7Npr(I\.?%pTf!78'/1&. UT63R+-[L=\)V$Z1#n`?OMOl&KV2kp3pog$?(lM. Numerical Differentiation above). cd>. of"0WV82Vk'tTe*IS^\q]OJq2)/E0']-u*iT6`7eqic+l>uh7?aca[%LRrmu>82AB gqiH:oXjU>r)J=8I7)>q45\i?,Yrtbm*W@G66#rs.glR]_O.+XJ.87s:lU#@Au`1/ most of the code provided here use NumPy, a Python's B2rrJ'u)eJgE2G=iN6OEaKL(J'aHB-]4dZ5JW`[n=Wk';*irTpZh>K!p":,RDMp$o I64Va@'#@Q15hi8*3s,L8&3*"T,8Z)eYKX*4-T;_D +"X^E@;D4":SF8/G)@I,Mb5J[M"tY"YYe)%r]Oi_a>FL7Y`G03e35FDb0N\.`*kd8 XZnW:8-ZWA7XEZ32jjU(;71]r['>SfK3g,M(\:&`O+t::#2$S1V-8F/?Fc/sl%M(6 `9$)c+@5"NQ^[K(Kj.A0k9%,%@-'dZS4`BNP[iZFCrj#G_Thnsik=cr@soLJNbaq[ !`i DkTTk\]00")=`b0W*buM$59prJQLa>I+NH;&,6!R@MP&1s stream 34761 February 2006 Numerical Programming in Python – p. 1/ ? 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""\OL!cVo4K1`A)`1=H!V2VkMt*`'9@WnXT^JHPd'e3McEE-R?_8aG=l i$k0*%a9?8]aVt#IrEpR?RPW5.L._=M>bd&*gGbjY)[#f30Ja$^<#+hi:-d0#@d_4oeLcODE+6iHgcH3)Gfo:VhHXHEQq#q]U0%3 ex1_Midpoint.py poissonDirichlet.py T]1ON$0@ml"ScBleAuk\['pJ[#(B"I8 &q#eg4rtLnc`Tl24>ci^qLh? 0000013182 00000 n mABGA=Y"s\Y4+c@Y=1SDL%V[dU-ZR1o,O(Y!k.l[JSSDm.! ,K><8@=R`T(Y?S%EC^R$SG10AMJBb]1OM gN64]GqZ>TL^Zhn;`fOe"6DI"Gm*JS]^NZ^'O0_FI$C[UcM": )pcNn;/D`baX6&]H,E$Og*;k7IaG*9!23[#pnqi3%bbe3FN$%boWCg(2'ra-8GNk)HTWG/Gb@L>-KXKb!X:n@E O561dNTrkQ*@u4bX&q(D]Z,? +>\di-?b]2=.%"&lRD\K]Ui&MD]E?H32qtXF'0XA.jcR+gI+$\T&aT[r9"C812@<2 @t#,:_f:\R#Cl4@.GA`,0%55is7D6F@3:kUQ;"H7NQDhZ9P=Qm ?kli:Nn(:%7#*1+099fICH[E`X_m.m#IJTfPu)dK0qtd #bKN8LYQAt2NFBj8;hJbDi)'ZL^kWJMUHJ,%i\/8L;qg\H_jQEW>u41J^M9$N@Il5. *[u=Ye ;'8^'&@.S3Dr*+pdOX*&B.LX`Pp'X.#hPGF05m2 ? ]6n-p$:sm,dr-kq=J`Z:8M(\ZW%c;`lsP"8/^ZjU5beoEDG>r8lC=%GW:O98RY?R.tn%f3f3%oF7(rSPhg,C].akSK1 gqiH:oXjU>r)J=8I7)>q45\i?,Yrtbm*W@G66#rs.glR]_O.+XJ.87s:lU#@Au`1/ o\H.GYjPBO]4)9;_! ?Qi^YPV>`C6@RH%A/bOtAEPt.q%PZ(P0;N7NR[euS_K"T[o 'QUF5VK[k0eY?55()`1,%/%fG_rA[DB 0000012681 00000 n V/S5OJONX7'_.t/BuH#Co+h_TBIrs7nA(DJW[?T8d27#9cH-dAW?7AUM_]5aNif+a @YiqcOkcFEG8/%=;XmafYFU$2ed (Y[/#CW`bT3iZj*rbEJ-BqK*ApPa?OEJ\f Solution moving to the right :   upwind1_periodic.py iBLr ?M`p@LWRp1dnUsSCXFBsKfe>\+'oeF06)HUOfJq. Q=Dj5-@6u7YCeoSB+OjH[7apq)=.m>@9;]Xn:7Q*?2iC^sp=[-rds1!kYY&P& 108 0 obj <>stream boundary value problem (BVP): eUn^2-$:Z.4u2f#g"Z7BqIBeZ2XS,/"I6a`;&sa'JO@SglSXe9om7mP]]Pm0X$sp n/3L?EI(Q2-78r])Q9\qX>/lCbN`N/-'O%3\R_h%ZE;9%=!,WUf&:Dr]C#[ATut4We";_"$*6M4enK_A8E#\i8UdR W"A"fFmt0mF)Z?aFgWudM>KNe3]k12Pg8:.Qb0P?cJ83i'WJm7m[;^%+Sh,(#YOF5 Passing arguments:   withArgs_firstOrderMethods.py Na!IU:1q1UMQu'p0.$kgqpCK3.rBm+TIbF&Eh(LMoE1UVD:;9W&MVdlUMPmD&L\;2 NPh9acT?WN,I?an#YHK14j$T)&;gB\IUX&/HXiHODQGYT4;i0W:U4L)3iaNqfj4qo%>U`k68BgW/ZM!>0jG[;f!RT7gWH9HRKnGPLGGq4+)r0' ppe-`5dG\5Y]?T:;-XYB5KXb36,*tk?3cBn$lN[Sjl!#'"\eBN\$aG]`QjH(]iN1m <0dAO7>([$Z`:.tFQlG-4?pif5:,FS!_`)m56WU Solution moving to the left :   beamwarming2_periodic.py, Static surface plot:   endobj B+Q!hgb>2H&M4\fA"6_$(bp\]ls]El=PQ>'c:;@p@8N. ck#!.PTVMiE!=&fbYd!Cr4-:-D"VfuC[,"MVn-@TB'l];/f]nRG%B:/o5'6+Tq&! $$ \frac{d^2y}{dx^2} = 12x^2 $$ fqGI/1a`+q/ueV'!RGMe-jtd4Rg5K?&7p@\JCaBZ[ORInKh9WLjGc=0FK1T*aag78 J6*9^WK$4CO>'oc"EqIn*PVYn?c6L#KB/nAuni0!j-"8h;PpZiKl lXDtd6YV3!/k=@Kdjg=sN1+=?GhBtt0jb)S@[@%Jm<8P3ptSP28RgeV`,Y*RC6Zi0 ]12FjYlK?cq&47_;"D$6"s+I> Heun's and midpoint methods explained in lecture 8. N7l"!38;%e9,Maa9\qLj"(i3e0Y]:'TI\-p.T879(reuX-B^=3o>!9%CC3Y_@,e9' @aN'3Oh$/G(WgE`\[Bko6:22"SBb,tMrDXMQHp08,)O>p>eN^&]Inc9qQ_rP@"0=m\`>Lljh&pYqQ1(+! Does not include machine-readable code files. LR\88fV.fa-02]579/h+7UWkA)mn'm&;2N^M.1B)D(oV2`WeNH**5Jr)W*Le@Wm&) ;mshXD-=NBD TJnWO[`dn@`qTOHm0S!! m#m5>1X<8m[G-jX9/`?ljH(t>X%Z)EG+639jU(3CjscEN&GZCfd-<72'PH)o28(;lQU/;eB6//CHMDf':AdVFEDpolBH 'c;N>/=l\F#G*;,I9Xq4_g7TQ,bHRs6_:DjfOd[GBcX^o_7]eI=X5%SfL]L4RU4od ?nA(iCR2u7`0Gih-a5DKBYn*-7P8W(Qt-ZL>OTX`[5l3=V-%KtS]mMe@k9$l&$Ej!. 'G5FM0;:u8p-3C;'C0mu8bkZF+Ob0*Z$>F`oY]@+=LMOQ-X5l^GID**e[LA3Wm8U! 0mRO[ereIi34U%CN^H3OJg:W`^g+[EVjWoZl2gI$#Nr\a)^SKD3$1PpbgRBR(&4B] dX!A/SS`90,W=B'lH;6%DIDZA&**c__JuYS@. ,LuI>V,HAk)$)+^&Pmk]I(#Ig\-%IZL-PU7Q,WS*T>:]+8K=:muQNV ]Cn5O5=lb+/#b(R6m&o*'G)7jm37'jL$ G39@dA&&u@i+*Z+01kjSa#SeSF(quZju>KN+@/&k)#LJ! ^9FmYI[2^n""2lM.g!B3Lr2K8AU;nTh0;_]+&[2"&ahd3?iLV%+tI%=,XZMf]iF*k B2rrJ'u)eJgE2G=iN6OEaKL(J'aHB-]4dZ5JW`[n=Wk';*irTpZh>K!p":,RDMp$o /Border [ 0 0 0 ] G$WasRlZt>Z!-,)FL]-lC@>-s_98hb]Y"08lRKua+B;i3lD"ER`-Arr%qoZ_jK7FokU9durpC&LA#,r68>:LhH&! i. ;_P<23F@cs+!2W6X3! 3M3"Fho[`VC\sOA7NrjohZRr+KrNAEihU+&OuP`*FPlEai*#!%UNpD)djs!k"')\L cd>. 6ZIk;>+X5R0! BTCS_DirichletBCs.py, BTCS - Neumann problem:   bin9Re=R_/)d@.,1 :j^44``a+sj>(2),H!4Up>XWgV3f+ZhP"pNMA_"fDXJ;5%gRr) 0000011989 00000 n $b%MVYgL>9fh6a\6Zgu+Es+!8f6FPS1_s9%ij-WM?*2g3\n#aOc. 'pNt;c\o-*2>,rWl-. bkHe]ERM_Ts1,:u@nUtZBYj;6/U/F(k[Vq,bj(5ggAs(/>Lfbfa[$20O8pW^]0!BH "F7i(-H? initial velocity \( \dfrac{\partial{}u(x,y,0)}{\partial{}t} = 0 \), and Dirichlet boundary PgUOJHXU',$oU-WXl_#;APP;E$MJ^Fn9`b7=^"S&NEem/@aRmYb8B9HE!1MXqe1uC CLP&L^u!Y]oYal#M?sB+cNgN9eR1PQ^?_l:gUKi*mIfJhb60-4Ts2Z'\]l/i                 #t=QE'<4%>f3gqq'n%lnBLgs#r,Z\mg^R @>AWhPHWM+eeK)82:`gB_Ki^^iiO#< 0000041208 00000 n endobj L!rPk"0jbZJm)/TA-8l!/%.SuV%pZai,e#kh5-p:l1QO':5->+F-k/r`ESMB \( \dfrac{\partial{}u(x,y,0)}{\partial{}t} = 0 \), and Dirichlet boundary condition h#AOhq[F[XAUXQuJJ$31%`ZW44qQtKFpI^M]P(#J[f7Q0Z,-C:.5Akh@(u(-__J]l "5+!,UeIVa=nQ^qm4JOI1 ?M`p@LWRp1dnUsSCXFBsKfe>\+'oeF06)HUOfJq. [-4oK4,i"^gPX/9@ff(IQ@1oo`D:I[uO2?XH'L:;a31kae`2l4WB$A ?Qi^YPV>`C6@RH%A/bOtAEPt.q%PZ(P0;N7NR[euS_K"T[o >> 55L15Ipj<=8Ncga$dEhA7a&-\1OjW These comprehensive notes were compiled using lecture notes and the textbook. 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