Numerical methods and solution, Summaries of Numerical Methods in Engineering

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2025/2026

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Fram o proof oni | Gee “ ——s Newlon Cole's Sean, Lot y= f00 be Funobion and do= Pte) Ya = Oo), Jas fbx), Jn = £040) By Newlon’s Forward formulas | ee bY + abe DO Bg. | y= $09 =Yo + TOY + a wher Ge oy NY ‘=Yot he NOY en Hoth > Put arate |v = {oder var ‘ + ¥r0 doren > [rowan hart : = h fit le 4yeh) drt - yaaa 14 UE) oy + (ei acian der: 1 = h[noy+ Pop 4 1 (ee) oy tb (ee se hee nay 7) eufon Cole's fonmuls general " Yo tn \ poate h| ny, +e aad aor an?) o* a Yo deat tsar (1 andpane)? y Baymole’ fel ie n= va r Redon, ba [yae- [ives $209 ae =h\2 Yo + 4 (M- -Y yi > : = AL Jo +4 Yn Ly | 2) sh [JoP-ato + Ly} ~ W| yo (4-2)+ bv] 4 , ~ h[ Ye yj oo | J) sin ah Yin), a | na un yan = h Tyr] Vine W Pad 2 in-\ *| Some Process dors " . J Ye [bo 4434.4} Me : Sy = Ay 44% 46) | i yd = A. ) Mne2 + Ayn yn “2. un de = Ky da Cortes to Wee te 2( Yaya ee tYn-2) FA] . | Simpgons +, voule Bin=3 » Simpson's 4. pule : | | oy J yan 3h lye syn) 49 (Y) Pet le Hts} * Fmt) 2 (ght 19}. tn-3) N=6, wedd leg reule! Mn . hoe J ye oc +541) + (ya yeya) + (ys F756) He io a + (Yg4 Bug) + Cb $6 19) Hite ay) tg + (assy) + (tid £oMe) + Cte FP Me)t Viste | # Baltes [raw by using” sim? gon'5.9 and BH dales rule: By Araperol? oo Yye roinh Wns “Tyra Yo =0 Yo = iyo? ¥ = — w= th Me ae OP 1g. yoroh= 2 | fos Ba ape. —+ Vig aot n= 3 = THE OF | Vg aM tae 4 U4 — aah = 0:05 99 | Ng = Yotbh= 5 = ered 26: 0385, % € YYh=6 re Tape * 6. 0OF: ICS} CamScanner Weddle’s Rule: \ Dn [ak Bhs + Ya bSI0 Ye beet YE) aie 2. Ji t5(0 $) po 24600) + 0.059845: (0 cae) | 40 oF) \.3F34% = t 204-26 @Graugs Jordan Melhed: +o. solve equ (RAvenes method of browses El Ey. Qlve by mes method: 6% —y4z=) wy te" ) jw }py-2> The augme o-[ a8) - £4 122 ] a -\: i | Po a / Ro—> Re re) ~7F -5 +A) ‘ 6 -9 -N ‘Fl jo Ry The syelem Of linea | ; . on. ; poe the System of equattan AX=B— ( 0) Fed aurenled. snaiix. foe ven Systeme) 3. Transform 'C) inte nopmad, fom - Normal means Convert he ; agonal elements into unity elements } ‘mination wethod ) 4-Find }he solution of equation - ote moctni x fon given system: Ri bie by ny Ce~nm14 0072 oO | O48 oO ob Asg, We 2 Ya, Zad i Wu-9y- 22 +4we 7 Bn ky t4z Hw eo wn Fy $32 k5w=s —6u +¢y ~z2-4w=5 Gia: “he Augmented matrix — CeniR= |b -9 ~-2 4 foo.) 4A | Ire Boe ~6 9 ~). —4 Ris &/5 a 49 04 0% a 4, 4 4 \\ oo #3 F JRaS Raw3hy, Usha -lOPy P4-> Rares! Qh. by a8 “Hodes o@ 4 0 64 BA Bb ei o MM oa = 8N : D> —2¢ 34 oe! 8 er Ro Ra/6-4 | jo apo +04 OF 314 o 64 OG] 25 134375 1-034 o th fF &e '-? 0 -2*9 44 gy 134 C~ 40) cleat me Ri hy TVERe 7 Res Rg—)) Rey 24 —> & }-2.2f5 Cv |} 1 0 | Woe 3.21995 | OF GIZA 0 4 OFI2H 13497 1 0.34345 0 Gg 93th ARG 910B 1 -421975 log ENO 4G IB 14875 wu se Rg> Rg /4 19975 108125 | 4.0695 QR. WSPS 0:72 | Ow 8 “Beis 144895 0-94 0 6 _ A 9.\F94 1) LVF '"PBSolo “\195 4 HG IE 294975 J ICS} CamScanner SE Geiss ob mela 7 at sel ti ne or equation ot ‘To: golve simwtneous |} System ,Consdah dhe Solera oF linear, equodjon* | ; Or we diy Hie dy On Ws bey }tgz= da 03 w + bey 4egz= ds Here, )ay | s |b | 1) |v) > lag) +124 \¢3 | S | \aa}+-|bs | e\ving equayion foe iY Z We 4, [a)-biy- oz] 5 yo 1b Leadon C07) — ee %; _ | d9- A3Y — bey) —( \ echo pub weyez=o wry -) wo \ Wal 4 Ee |O%—bYy-2z=3 4M —)oy}32=-3 ww 4+6y Floz=-3 = ap [272 > [3 - ante) = E3-t-6y) Weer 7 = poe ~ 0:2 1 +. x[3t +o] | ve [2 of ot we oct nyJ arma mare Value ag M3 f Solving eduetion tow yz: We pet tins} approximate Value ag M1554. Ttenodion 2: Pct ws ky v= Vi Zest Ito iti, we pe} second Approximate \ue as 0) Yo /% Heradion 3 : Ad wmv) Y=Y2 -2=Z2 ire ly, ‘| vee 23 Until two decimak Place Js selling matched, op -O1- ss era Abas ii nallo | tH Gauss Eliminadiop. method Workin’ tule ' 1 Dtonsider re cyclen of equation Orn, Vory paz= 4d ! ag bboy Henze 4% Qn + boy +C92= 93 le AX=B° | = SEB) fs en o 2) Find augmented matrix ont 4) 2) “Traunchor™ who upper \ofanguler Sonm/ Echelon p | rangalan/ @) Fd equal aortnes PO Mhy +n Echelon mode eal ) nd co\” of yen eC ion Ey: 2¥~ ypg Zr? yw Yt yZ= MW Lyt Le 2. aA y 24 y L-18 Zz Bugmerted modniy ‘ O wry pen & - 4a i az <=6 7? = A, Cs La:B) = al 4 4 f 3 Q6-64-26 © Sai Seibel eFal 1: Consider the system of linea abe eek -G,z=d, A2M toy + Caz =d 99h +bsy4 ea2= ia a 2: Solve a equation Wy? oy La by - CZ) Sy 3. Foe fish apprexiwile valus put y=z20 Int) ind vert a ky vem vod 226 in Gi) Find y= eV ) F Ow Y= ond YY ink (itl) Bnd 2-2 ond approxinude ; pd inl) yo Ya 2=kh and find vay , in (ii) YrN2) 222\ Gnd ind ye =| pur in (i) Mehr) Ye, find Leaky repent © By ¥3n HIy—42=95 are eye a FMS Bayh} 2 =104 | BN $y 992274 Wz wespectivoaly — wed, [on -iy+42] —O 9 =; [loa 7-192] —O z= ds Qi- re © Fisd- pu, Meyez=0 in 7) “= oy [on- oo] = \145 Y= by flor F149) -2 =\:246 , ) \8 oD Z= dy fea 3Ch 49) -9.(11 246) After Ast ieradtion , eb l45, Yahoo Zs he24 imate PICO MH >) ; ; , Ond ag le - &, WF _n fier 4 U2) 9 ‘ Yo [lo4 (1145) 190924 J ~ \,992 we ta 9 (45) ~ a (nese) = V4? 2 gg Ht nfler ond -\ereation, i... Yo = 098% You) 992, Vaal 729