Kodi njira Simpson, ndi mmene kukhazikitsa mu chinenero Pascal

Kuwerengetsa ubwino ndi yofunika, ngakhale pafupifupi, pali njira zabwino dzina la Mlengi wake - njira ya Simpson. Iye amatchedwanso parabolas njira, chifukwa amagwiritsa ntchito yomanga parabola a. chithunzi ichi chili mbuuku pafupi zotheka kugwira ntchito. Kwenikweni, njira bwanji kumanga parabola lomwe limasonyeza lifanane ndendende ndi mfundo za kugwira ntchito, Sikutheka ndi yofunika ndi approximated. Chilinganizo malo malire ake ndi ndi b zikuwonekera apa: 1 / h * (Y + 4y _{0 1} + 2y ₂ + 4y ₃ + ... + 4y _N-1 + Y _n). Pano, tikufuna kuwerengera lililonse Y kuchokera 0 kuti N, kumene N tingamasulire tokha - kwambiri, ndi bwino, chifukwa kwambiri Y-m, kwambiri oyerekeza kuti phindu lenileni la ntchito yathu. Mokhudzana ndi H, kenako stepi ino kuchita masamu ndi chilinganizo zotsatirazi: (Ba) / (n-1).

Akuti zonse ndi wosavuta, koma zingakhale zofunikira kukhazikitsa zonsezi ntchito. Pakuti mapulogalamu ambiri palibe njira yabwino yothetsera vutoli, monga njira Simpson - Pascal kapena Delphi. Mu chilengedwe, n'zosavuta kwambiri osati kuonanso bwino integral, komanso kumanga Zithunzi za ntchito kuti izo, ndipo ngakhale anamanga oimba ng'oma pamodzi ndi iye. Choncho, tidzamva mmene inu mwamsanga kukhazikitsa njira Simpson ndipo ngakhale kufotokoza, ngati n'koyenera, onse apa ndi chimene bungwe, ofuna onse.

Koma ine ndikukumbukira chimene chimaoneka izi zisanachitike yofunika. chithunzi ichi, chimene njanjira ndi mizere kuyambira ndi 'X' olamulira, i.e. ndi b.

Choncho, kuyamba pulogalamu muyenera kulenga ntchito kwa ntchito integrable (kukhululukira tautology), zomwe amangowerenga kulemba f: = ndi chinachake chimene ife tidzapeza yofunika. Apa, n'kofunika kwabasi kuti molakwika kulowa ntchito mu Pascal. Koma ndi nkhani yosiyana. Ndondomekozi chifukwa adzayang'ana motere:

Ntchito f (×: weniweni): chenicheni;

Ndi mbali zofunika lemba

ayamba

f: = 25 * Ln (x) + tchimo (10); {Apa ndipo muyenera kulemba nkhani za ntchito zake}

kutha;

Kenako lembani ntchito ndi kukhazikitsa njira Simpson. Start chidzakhala chinachake monga:

Ntchito simpsonmetod (a, b: chenicheni; N: inteja): chenicheni;

Kenako, ife kulengeza zosintha:

var

m: chenicheni; {Subtotals (kupitiriza kumvetsetsa)}

H: chenicheni; {Gawo}

wanga: inteja; Monga {kauntala}

mno: inteja; {} The kuchulukitsa lotsatira

Ndipo tsopano, Ndipotu pulogalamu yokha:

ayamba

H: = (Ba) / (n-1); {Amafuna sitepe malinga ndi chilinganizo muyezo. Nthawi zina sitepe kwalembedwa mu ntchito, mu nkhani iyi, chilinganizo Izi sizikhudza}

m = f (b) + f (a); {Popeza koyamba mtengo phula}

mno: = 4; {Kumbukirani chilinganizo - 1 / h * (Y + 4y _{0 1 ...} kuti 4 apa ndi alembedwa, chinthu chachiwiri ndi 2, koma zambiri lino}

Tsopano zofanana chilinganizo:

wanga: = 1 N-2 chiyani ayamba

m = s + mno * f (a + H * Mu); Powombetsa {kuwonjezera chinthu china kuchulukitsa ndi 4 * Y _N kapena 2 * Y _N}

ngati (mno = 4) ndiye mno: = 2 china mno: = 4; {chinthu Izi zimasiyanasiyana ndipo - ngati tsopano 4, limasintha 2 ndi mosemphanitsa}

kutha;

simpsonmetod: = m * H / 3; Kenako {mkombero chifukwa ndalama ndi kuchulukitsa ndi H / 3} malinga ndi chilinganizo

yotsiriza.

Ndi zimenezo - kuchita chilichonse malinga ndi njira. Ngati inu mulibe asanaganize mmene tingagwiritsire ntchito mu njira yaikulu pulogalamu Mwachitsanzo Simpson zingakuthandizeni ndi ichi.

Choncho atalemba ntchito zonse lemba

Yambani

N: = 3; Tinakhala {N}

Q: = simpsonmetod (a, b, n); {Popeza njira Simpson ndi kugwira ntchito zowerengetsa ndi yofunika kwambiri kuti B, padzakhala zinthu zingapo mawerengedwe, kotero kukonza mkombero}

kubwereza

q2: = Q; {Analoweza sitepe yapita}

N: = N + 2;

Q: = simpsonmetod (a, b, n); {Ndipo} phindu kuchita masamu motere

mpaka (ABS (Q-q2) <0.001); {Kulondola kolowera kwalembedwa, kotero mpaka mufika molondola chofunika, m'pofunika kubwereza zochita yemweyo}

Apa ndi iye - njira Simpson. Ndipotu kanthu kobvuta, zonse zinalembedwa mofulumira kwambiri! Tsopano kutsegula wanu Turbo Pascal ndi kuyamba kulemba dongosolo.