METODOS NUMERICOS INTEGRACION, Diapositivas de Métodos Numéricos

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MÏQIAIV H^MÏUOFIVMÏQIAIV H^MÏUOFIV

OHQNJUDFOÖHOHQNJUDFOÖH

H^MÏUOFDH^MÏUOFD

Aifnhtn<Aifnhtn<

@of. Ludh Fdris Opdhdquï Wddfois@of. Ludh Fdris Opdhdquï Wddfois

ïtiaisïtiais nmpndaisnmpndais dhtnsdhtns anan dd nrdnrd anan dsds fimputdairdsfimputdairds

Ohtnjrdfoöh jräbofdOhtnjrdfoöh jräbofd

• • Vn jräbofd d buhfoöh siern uhd fudarofud y sn funhtdh nhümnri an fudarisVn jräbofdd buhfoöh siern uhd fudarofud y sn funhtdh n hümnri an fudaris

qun dprixomdh närndqun dprixomdh n ärnd

• • Nh hümnri an fudaris mutopofdai pir närnd anis fudaris ns uhdNh hümnri an fudaris mutopofdai pir närnd anis fudaris ns uhd

dpridprixomdfoöh anärndxomdfoöh an ärnd edli dedlid furvdfurvd

EdrrdsEdrrds

• • Vn aovoan närnd nh edrrds vnrtofdns, fih uhd dturd ojud dvdir an d buhfoöhVn aovoan n ärnd nh edrrds vnrtofdns, fih uhd dturd ojudd vdir and buhfoöh

nh npuhti mnaoi an fdad edrrd. @d sumd an ärnd an is rnftähjuis ns uhdnh npuhti mnaoi an fdad edrrd. @d sumd an ärnd an is rnftähjuis ns uhd dpridprixomdfoöh anärndxomdfoöh an ärnd edli dedlid furvdfurvd

Börmuds an Hnwtih-FitnsBörmuds an Hnwtih-Fitns

• •

Vn edsdh nhVn edsdh nh d nstrdtnjofimpofdad i adtis aosfrntis fih uhd buhfoöh dprixomdadfimpofdad i adtis aosfrntis fih uhd buhfoöh dprixomdadd nstrdtnjod an rnnmpdzdr uhdd an rnnmpdzdr uhd buhfoöhbuhfoöh

qun sndqun snd bäfoan ohtnjrdrbäfo an ohtnjrdr

aihanaihan bbhh((xx) ns uh piohimoi an) ns uh piohimoi an d birmdd birmd

• • @d ohtnjrdsn punan tdmeoïh dprixomdr mnaodhtn uhd snron@d ohtnjrd sn punan tdmeoïh dprixomdr mnaodhtn uhd snron

an piohimois dpofdad pir pnadzis d d buhfoöh ian piohimois dpofdad pir pnadzis dd buhfoöh i adtissiern snjmnhtis an ihjotuasiern snjmnhtis anihjotua fihstdhtfihstdhtnn adtis

  ^   

ee

dd

hh

ee

OO dd bb xx axax bb xx axax

 

hh hh

hh bb (^) hh xx  dd dd xxdd xx  ddhh xx  dd xx 44 44

55 (^77 4455) 

Börmuds an Hnwtih-FitnsBörmuds an Hnwtih-Fitns

• • Vn aospihn anVn aospihn an birmds fnrrdads y deonrtds an börmuds an Hnwtih-FitnsFitns birmds fnrrdads y deonrtds an börmuds an Hnwtih-
• • BIUMDV FNUUDADV< sih dqunds aihan `is adtis d` ohofoi y d` bohd`BIUMDV FNUUDADV< sih dqunds aihan is adtis d ohofoi y dbohd an isomotns anan isomotns an ohtnjrohtnjrdfoöh sih fihifoaisdfoöh sih fihifoais
• • BIUMDV DEONUQBIUMDV DEONUQDV< tonhnhDV< tonhnh omotns an ohtnjrdfoöh qun snomotns an ohtnjrdfoöh qun sn nxtonhanhnxtonhanh

mäs dä an` rdhji an `is adtismäs dä anrdhji anis adtis

• • Hi sn usHi sn usdh pir dh piri jnhnrdpdrd ohtnjri jnhnrd pdrd ohtnjrdfoöh anbohoaddfoöh anbohoad
• • Voh nmedrji, sn utoozdh pdrd nvdudr ohtnjrdns ompripods y nhVoh nmedrji, sn utoozdh pdrd nvdudr ohtnjrdns ompripods y nhdd siufoöh an nfudfoihnsiufoöh an nfudfoihns aobnrnhfodns iraohdrodss aobnrnhfodns iraohdrods

Nlnmpi.Nlnmpi.

Fdfudr<Fdfudr<

   <<//^ 

 

pir nmïtiai an trdpnfoipir nmïtiai an trdpnfoi

Viufoöh.Viufoöh.

 ==  == 44 ⟲⟲  44 == 77..>>

 == ^ == 55 ⟲℈℈ == 5⟲ 5 ∕∕ 4 5 4 5 == 6.6.64646:6:73 73 44

== 4 4

rnmpdzdhai<rnmpdzdhai<

 ==        ≎≎ ℈℈ 5 5   +()  +()  = 4.?723>1 = 4.?723>

Dpofdfoöh mütopn and rnjd QrdpnzioadDpofdfoöh mütopn and rnjd Qrdpnzioad

• • ^hd birmd an mnlirdr d nxdftotua and^hd birmd an mnlirdr d nxdftotua and rnjd trdpnzohtnrvdi an ohtnjrohtnrvdi an ohtnjrdfoöh [d,e] nh uhdfoöh [d,e] nh uh hümnri an snjmnhtis y dpofdr nhümnri an snjmnhtis y dpofdr nrnjd trdpnzioadns aovoaorioad ns aovoaor nn mïtiai d fdad uhi an nismïtiai d fdad uhi an nis
• • @ds ohtnjrdns anis snjmn@ds ohtnjrdns anis snjmnhtis sn sumdhhtis sn sumdh pdrd ietnhnr d ohtnjrd anpdrd ietnhnr d ohtnjrd an

d buhfoöh nh [d,e]d buhfoöh nh [d,e]

• • Vo cdyVo cdy^ hh+4 puhtis edsn ojudmnhtn nspdfodais (+4 puhtis edsn ojudmnhtn nspdfodais (^ xx 77 , x, x 44 , x, x 55 ,…,…^ xxhh),), nhtihfns cdynhtihfns cdy hh snjmnhtis an ojudsnjmnhtis an ojud dhfcurd;dhfcurd; c =c = ((e-de-d))/h/h
• • Vo d y e sih ansojhdais fimiVo d y e sih ansojhdais fimi xx 77 yy xxhh, rnspnftovdmnhtn d, rnspnftovdmnhtnd ohtnjrdtitdohtnjrdtitd sn rnprnsnhtd fimisn rnprnsnhtd fimi

  ^   ^    

   

hh

hh

xx

xx

xx

xx

xx

xx

OO bb xx axax bb xx axax bb xx axax

44

55

44

44

77



Dpofdfoöh mütopn and rnjd QrdpnzioadDpofdfoöh mütopn and rnjd Qrdpnzioad

• • Vustotuynhai d rnjd trdpnzioadsn ietonhnVustotuynhaid rnjd trdpnzioad sn ietonhn
• • Djrupdhai tïrmohis sn ietonhnDjrupdhai tïrmohis sn ietonhn
• • Qdmeoïh sn punan nxprnsdr fimiQdmeoïh sn punan nxprnsdr fimi

            55 55 55

OO  cc bb xx^77  bb xx^44 cc bb xx^44  bb xx^55  cc bb xxhh^ ^44  bb xxhh

     

   





hh

hh

oo

bb xx bb xxoo bb xx

cc OO

44

44 55 77 55

 

     

hh

bb xx bb xx bb xx OO ee dd

hh

hh

oo

oo

55

55

44

44







Viufoih.Viufoih.

 - ℈℈ ==^4 4 ∕∕ ((∕ 22 ∕4 4))==^4466 = 7.666666= 7. 

• 77 d=S7d=S7 -4-4 7.514?:47.514?: oo xoxo b(xo)b(xo)
• 44 S4=S7+cS4=S7+c -5/6-5/6 7.64?1137.64?
• 55 S5=S4+cS5=S4+c -4/6-4/6 7.6::6367.6::
• 66 S6=S5+cS6=S5+c 77 7.6?3?157.6?3?
• 11 S1=S6+cS1=S6+c 4/64/6 7.6::6367.6::

• S>=S1+cS>=S1+c 5/65/6 7.64?1137.64?

• 22 S2=S>+cS2=S>+c 44 7.514?:47.514?:
  •  == 7.6666667.666666 55 7.7.51514?4?:4 = 7.2:34?4 = 7.2:34?4:4++55 4.4.:?:?52 5271 71 ++7.7.51514?4?:4:

Dpofdfoöh mütopn and rnjd QrdpnzioadDpofdfoöh mütopn and rnjd Qrdpnzioad

• • ^h nrrir pdrd d rnjd trdpnzioadan mütopn dpofdfoöh sn punan ietnhnr d^h nrrir pdrdd rnjd trdpnzioad an mütopn dpofdfoöh sn punan ietnhnr d

sumdr is nrrirns ohaovoaudns an fdad snjmnhti pdrd adrsumdr is nrrirns ohaovoaudns an fdad snjmnhti pdrd adr

• • Nstn rnsutdai sn punan sompobofdr dnstomdrd mnaod an d snjuhad anrovdadNstn rnsutdai sn punan sompobofdr d nstomdr d mnaod and snjuhad anrovdadpdrd tiai nohtnrvdi fimipdrd tiai nohtnrvdi fimi
• • (^) Tunadhai nnrrir an truhfdmonhti fimiTunadhai n nrrir an truhfdmonhti fimi
• • Dsí, so nhümnri an snjmnhtis sn aupofd, nnrrir an truhfdmonhti aosmohuorä dDsí, so n hümnri an snjmnhtis sn aupofd, n nrrir an truhfdmonhti aosmohuorä d uh fudrtiuh fudrti

 

 ^  hh oo tt (^) hh bb oo NN ee dd (^6644)

66 '' '' 4545



hh

bb bb

hh oo

 oo  ^44

'' '' ''''



4545 55

66 bb hh

NN ee dd dd

^ 

Nlnmpi.Nlnmpi.

Fdfudr<Fdfudr<

   <<//^ 

 

pir nmïtiai an Vompsih 4/6pir n mïtiai an Vompsih 4/

Viufoöh.Viufoöh. WdrWdrd nmïtiai an Vompsih 4/6d n mïtiai an Vompsih 4/6 nvdir an h=5nvdir an h=

℈℈ ==

 ∕∕ 



==

5 5 ∕∕4 4

55

= 7.>= 7.>

 =  = 4=  = 4  44 == 7.>7.>

 ==  ++℈ =℈ = 44 ++ 77..>> = 4= 4..>>  4.>4.> == 4.>4:7534.>4:

^ == ^ ++℈ =℈ = 44..>> ++ 77..> => = 5 5  55 == 6.646:736.646: rnmpdzdhai<rnmpdzdhai<

 ==      



 (^) ≎≎ ℈℈ 6 6  ^ +1 +1 ^ +(+())

 ==

7.>7.>

66

7.>+1 4.>4:753 +6.646:737.>+1 4.>4:753 +6.646:

 = 4.212?:7 = 4.212?:

Dpofdfoöh mütopn and rnjd an Vompsih 4/6Dpofdfoöh mütopn an d rnjd an Vompsih 4/

• • @d rnjd an Vompsih 4/6 sn@d rnjd an Vompsih 4/6 sn punan mnlirdr daovoaor n ohtnrvdi anpunan mnlirdr d aovoaor nohtnrvdi an ohtnjrdfoöh nh uh hümnri an snjmnohtnjrdfoöh nh uh hümnri an snjmnhtis an ojuddhfcurd,htis an ojud dhfcurd, (^) c =c = ((e-de-d))/h/h
• • @d ohtnjrdtitd sn punan rnprnsnhtdr fimi@d ohtnjrdtitd sn punan rnprnsnhtdr fimi
• • Vustotuynhai d rnjd an Vompsih 4/6Vustotuynhai d rnjd an Vompsih 4/
• • Fimeohdhai tïrmohisFimeohdhai tïrmohis

  ^   ^    

hh

hh

xx

xx

xx

xx

xx

xx

OO bb xx axax bb xx axax bb xx axax 55

11

55

55

22

11 22 55

11 22 55

11 55

77 44 55 55 66 11 bb xxhh 55 bb xxhh 44 bb xxhh cc

bb xx bb xx bb xx cc

bb xx bb xx bb xx OO cc

   

  

  

  

  ^ ^ ^ ^ ^ ^ ^ 

11 55

55

55 ,, 11 ,, 22

44 (^77 44) ,, 66 ,,>> hh

hh

ll ll

hh

OO  cc bb xx  oo^  bb xxoo^   bb xx  bb xx









Vn anen usdr uhVn anen usdr uh hümnri pdr anhümnri pdr an snjmnhtis pdrdsnjmnhtis pdrd ompnmnhtdr nompnmnhtdr n

66 mïtiaimïtiai

Nlnmpi.Nlnmpi.

Fdfudr<Fdfudr<

  ;; // ;; 

pir nmïtiai an Vompsihpir n mïtiai an Vompsih 4/6 fimpunsti pdrd h=24/6 fimpunsti pdrd h=