Numerical Computing Lab 2

7/31/2019 Numerical Computing Lab 2

1/25

Cif 6? Mlttkbm ptivtld }kth GITCIF 9 sZ i m l

B|glvkìc @agz|tkbm Zvlzivld f{? Lbmv" Iigbi Ehickd

AFOL@TK^L? Nigkckivkitkab }kth GITCIF? |bdlvptibdkbm ha} ta vlid ibd }vktl diti#

ivvi{ ~ivkifclp ibd githlgitkìc n|b`tkabp ibd dl~lcazkbm g'nkclp"

6"9 VLIDKBM IBD ]VKTKBM

Zippkbm diti ta ibd nvag GITCIF kp zappkfcl kb pl~lvic dknnlvlbt }i{p" Thl glthadp gi{ fl`cippknkld kbta thvll `cipplp?

(i+ Kbtlvi`tk~l azlvitkab f{ el{faivd av ga|pl

(f+ Vlidkbm nvag av }vktkbm ta i diti nkcl

(`+ \pkbm pi~lp av caid

Kb thl vlgikbdlv an thkp p|fpl`tkab# abc{ i gkbkgic iga|bt an kbnavgitkab vlmivdkbm vlidkbm ibd}vktkbm kp kbtvad|`ld" Gavl kbnavgitkab ìb fl na|bd kb Pl`tkab 9"8"

kbz|t? GITCIF ìb tiel kbz|t diti thva|mh thl el{faivd |pkbm thl kbz|t àggibd" Ta vlid i

b|gflv# thl p{bazpkp }a|cd fl

7 kbz|t(-T{zl {a|v kbz|t?+

Thl ptvkbm flt}llb y|atl pkmbp# biglc{# T{zl {a|v kbz|t?# kp i zvagztkbm glppiml ta fl zvkbtld

a|t ab thl p`vllb" Ip i ~ic|l kp t{zld ibd i vlt|vb el{ kp hkt# thl kbz|t kp pi~ld kb " I ptvkbmkbz|t ìb fl t{zld nvag thl el{faivd" Thl p{bazpkp kp

7 kbz|t(-[a|v bigl zclipl? -#-p-+

Thl plàbd ivm|glbt pkbdkìtlp thit thl kbz|t nvag thl el{faivd kp i ptvkbm" Thl ~ivkifcl flàglp ib ivvi{ ~ivkifcl (va} ~l`tav+ |bclpp thl ptvkbm hip abc{ abl `hivi`tlv" I ptvkbm kbz|t

ìb fl tielb f{ kbz|t }ktha|t -p-kn thl t{zld ptvkbm kp lb`capld f{ pkbmcl y|atl pkmbp" Kb thkp ìpl#i zvagzt glppiml gi{ fl }vkttlb ip

7 kbz|t(-T{zl {a|v bigl kb pkbmcl y|atl pkmbp?-+

nzvkbtn?

Thl nzvkbtn ptitlglbt zva~kdlp àbtvac thl }i{ thit b|glvk` ibd ptvkbm diti ivl zvkbtld ta thlàggibd }kbda} av i nkcl"

Thl p{btix an nvzvkbtn kp fipld ab thl nzvkbtn n|b`tkab nvag thl @ cibm|iml#

nzvkbtn(navgit# ~ivkifclp+

nzvkbtn(nkd# navgit# ~ivkifclp+


2/25



}hlvl navgit kp i tlxt ptvkbm thit àbtvacp thl izzlivib`l an thl a|tz|t# ~ivkifclp kp i àggi'plzivitld ckpt an ~ivkifclp ta fl dkpzci{ld i`àvdkbm ta thl pzl`knkìtkab kb navgit# ibd nkd kp i nkcl

kdlbtknklvnav thl nkcl ta }hk`h thl a|tz|t kp plbt" Thl ~ic|l an nkd kp abc{ plt }hlb a|tz|t kp plbtta i nkcl"

P|ggiv{ an navgit àdlp nav |pl }kth nzvkbtn

@adl @ab~lvpkab kbptv|`tkab

,p navgit ip i ptvkbm

,d navgit }kth ba nvi`tkabic zivt (kbtlmlv navgit+

,n navgit ip i ncaitkbm'zakbt ~ic|l

,l navgit ip i ncaitkbm'zakbt ~ic|l kb p`klbtknk` batitkab

,m navgit kb thl gapt àgzi`t navg an lkthlv ,n av ,l

Sb kbplvtp bl}ckbl kb a|tz|t ptvkbm

St kbplvt tif kb a|tz|t ptvkbm

@abtvacckbm Nklcd ]kdth ibd Zvl`kpkab

Thl ,dibd ,p navgit pzl`knklvp ìb fl gadknkld ta àbtvac thl nklcd }kdth |pld ta dkpzci{ i

~ic|l" Thkp kp flpt lxzcikbld ~ki lxigzcl" P|zzapl thit thl e ibd p ~ivkifclp ivl ippkmbld ~ic|lp

e 7 6R=5 p 7 -fkm vld fivb-5

]ktha|t pzl`kn{kbm i nklcd }kdth thlpl nklcdp ivl dkpzci{ld }kth thl gkbkg|g nklcd }kdth# k"l"#thl gkbkg|g b|gflv an `hivi`tlvp bl`lppiv{ ta dkpzci{ thl àbtlbtp an thl ~ivkifclp"

nzvkbtn (,dSb# e+

968

nzvkbtn(,pSb-# p+

fkm vld fivb

Thl nklcd }kdth pzl`knklv kp ib kbtlmlv thit zvl`ldlp thl d kb ,d av thl p kb ,p" Nav lxigzcl# tazvkbt thl ~ic|l an e }kdth an > `hivi`tlvp |pl thl ,>d navgit"

nzvkbtn (-,>d Sb c604=8; Sb- #e+

968

9604=8;


3/25



Thl pl`abd ckbl an a|tz|t gielp kt lip{ ta pll thit thl ~ic|l an 968 kp ab thl vkmht'hibd lbd an inklcd thit kp pkx `hivi`tlvp }kdl" Pkgkcivc{

nzvkbtn(-,>p Sb c604=;8:9604=8;:Sb-#p+

fkm vld fivb

9604=8;:9604=8;:

Zvkbtkbm a|t navgittld glppimlp ibd b|gflvp kp zappkfcl |pkbm nzvkbtn5 nav lxigzcl#

nzvkbtn (-Thl ~ac|gl an thl pzhlvl ,96"


4/25



~ac7


5/25

Cif 6? Mlttkbm ptivtld }kth GITCIF < sZ i m l


6":::: 9">::: 9"6::: :"8::: :"4::: ':"::::

Thl dlnkbktkab an i `ac|gb ivvi{ kp pkgkciv ta i va} ivvi{ lx`lzt thit thl lclglbtp ivl plzivitld

f{ plgk`acabp5 nav lxigzcl#

7 U:5 :"95 :"65 :"05 :"45 :"


6/25

Cif 6? Mlttkbm ptivtld }kth GITCIF > sZ i m l


`(c?6?=+7# =# '6# 9# =# 4# '># 8# 4# :# '6W5

xgkb7;;;5

xgix7';;;5

nav k7c?clbmth(x+5


14/25



kn xgkb2x(k+# xgkb7x(k+5lbd

kn xgix3x(k+# xgix7x(k+5lbd

lbd

Uxgkb# xgixW

Thl ibp}lv kp

ibp 7

'> ;

Lxigzcl 6"6

(i+ ]vktl i p`vkzt ta lxigkbl kn i mk~lb b|gflv kp i zvkgl b|gflv av bat" Vlid thl kbtlmlv ta fl

lxigkbld f{ thl kbz|t àggibd" Da bat |pl ni`tav av kpzvkgl àggibdp" (Hkbt? @hlè ta pll kn

thl b|gflv kp dk~kpkfcl f{ icc thl ca}lv b|gflvp lx`lzt |bkt{+"

(f+ ]vktl i p`vkzt ta zvkbt a|t thl zvkgl b|gflvp clpp thib 9:: kb kb`vlipkbm avdlv" Zvkbt a|t thltatic b|gflv an thl zvkgl b|gflvp na|bd# i ckpt an thl zvkgl b|gflvp# ibd thl p|g an thl zvkgl

b|gflvp clpp thib 9::" (Da bat |pl ni`tav av kpzvkgl àggibdp+"

Pac|tkab

(i+ Kb thl nacca}kbm p`vkzt# thl b|gflv ta fl lxigkbld# k# kp mk~lb thva|mh thl kbz|t" Thl ibp kpkbktkickld ta 9" Thlb thl b|gflv k kp dk~kdld f{ 6 thva|mh k'9" Kn n kx(k!b+ ly|icp k!b nav ib{ b# ibp

kp plt ta : ibd thl caaz kp tlvgkbitld f{ fvlie" Kn thl caaz kp àgzcltld }ktha|t vlplttkbm ibp7c#thl k kp i zvkgl b|gflv"

`cliv

k7kbz|t(-T{zl ib kbtlmlv mvlitlv thib 9? -+5

ibp7c5

nav b76?k'c

kn k!b77 n kx(k!b+ # ibp7:5 fvlie5lbd

lbd

kn ibp77:# nzvkbtn (-Ba# =#6" An kp bat i zvkgl b|gflv" Sb- #k+

lcpl nzvkbtn (-[lp# ,6":n kp i zvkgl b|gflv" Sb- #k+

lbd

I pigzcl a|tz|t kp


15/25

Cif 6? Mlttkbm ptivtld }kth GITCIF 9< sZ i m l


T{zl ib kbtlmlv mvlitlv thib 9? HA] TA ]VKTL [A\V A]B N\B@TKABP

N|b`tkabp kb GITCIF# }hk`h ivl pi~ld ip plzivitl g'nkclp# ivl ly|k~iclbt ta p|fva|tkblp ibdn|b`tkabp kb athlv cibm|imlp"

n|b`tkab thit vlt|vbp abc{ abl ~ivkifcl? Clt |p `abpkdlv i n|b`tkab g'nkcl nav thl nacca}kbm

ly|itkab?

(6"9+

Ipp|gkbm thl g'nkcl kp pi~ld ip dlganQ"g# ktp p`vkzt kp kcc|ptvitld f{

Ckpt 6"

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Numerical Computing Lab 2