He aha te mea te tikanga Simpson, me pehea ki te whakatinana i te reira i roto i te reo Pascal

Ki te tātai i te uara o te wāhi, ahakoa āwhiwhiwhi, i reira he he tikanga pai, ko muri i tona kaihanga - te tikanga o Simpson. ka karanga ano ia parabolas tikanga, no te mea whakamahi reira te hanga o te unahi. hāngai ana tēnei ahua te rite tata rite taea ki te mahi. Mau, te ara me pehea ki te hanga i tētahi unahi, e tohu hāngai rite ki nga ngā o te mahi, e taea ai, a ka approximated te wāhi kei te. rite tenei wāhi Tātai o ona rohe ki te me te b titiro: 1 / h * (y + 4y _{0 1} + 2y ₂ + 4y ₃ + ... + 4y _n-1 + y _n). Here, Me tika tatou ki te tātai ia y i 0 ki te n, n tautuhi tatou ia tatou iho te wahi - te ake, te pai, no te mea te atu y-s, te atu āwhiwhiwhi ki te uara pono o to tatou mahi. Ki te whakaute ki te h, a ka tatau i tenei taahiraa e te tātai e whai ake nei: (ba) / (n-1).

I roto i te ariā, ko tino ohie mea katoa, engari e te mea e tika ana ki te whakatinana i te katoa o tenei i roto i te mahi. Hoki hötaka maha he kahore ara pai ki te whakaoti i tenei raruraru, kia rite ki te tikanga o Simpson - Pascal Delphi ranei. I roto i tenei taiao, ko reira tino ngāwari kore anake ki te arotake i te wāhi, engari ano hoki ki te hanga i te kauwhata o te pānga ki reira, a tae noa hanga tona trapeze. Na, titiro matou ki te pehea koe e taea e hohoro whakatinana i te tikanga o Simpson me tae noa ki te whakamārama, ki te hiahiatia, e rua i konei, ka whakaritea e te, te hunga hiahia katoa.

Ko mahara ahau rite te aroaro o tenei wāhi aha titiro reira. Tenei ahua, rohe nei e ngā raina timata ki te tuaka 'X', i.e. he me b.

Na, ki te tīmata i te hōtaka e hiahia ana koe ki te waihanga i tētahi mahi mō ngā mahi integrable (te whakarere noa te tautology), e noa i ki te tuhituhi f: = me te tahi mea mo e e kitea e tatou te wāhi. Here, Ko reira mahu'inga kore ki te kotiti i roto i te tomo i te mahi i roto i Pascal. Ko te reira i te aamu rerekē. Ka titiro te waehere hua te tahi mea rite tenei:

f mahi (x: tūturu): tūturu;

Na nga āhuatanga kuputuhi taketake

timata

f: = 25 * ln (x) + hara (10); {Here a hiahia koe ki te tuhituhi i te tirotiro o ona mahi}

mutu;

Na ka tuhituhi i tētahi mahi ki te whakatinana i te tikanga o Simpson. ka waiho Tīmata te tahi mea rite:

simpsonmetod mahi (he, b: tūturu: n: tōpū): tūturu;

Next, e whakaatu tatou te taurangi:

var

s: tūturu; {Tapekeroto (matau atu)}

h: tūturu; {Hipanga}

toku: tau tōpū; Just {counter}

mno: tau tōpū; {} Ko te multipliers muri

Na inaianei, i roto i te meka, ano te hōtaka:

timata

h: = (ba) / (n-1); {Ka puta taahiraa rite ki te tātai paerewa. I te tahi taime te taahiraa i tuhituhia i roto i te mahi, i roto i tenei take, e kore e tenei tātai tono}

s: = f (b) + f (he); {Homai uara te ware tuatahi}

mno: = 4; {Kia mahara ki te tātai - 1 / h * (y + 4y _{0 1 ...} e tenei 4 konei, ka rai, te rua o nga take ko te 2, engari atu i runga i tenei i muri}

Na i taua tātai taketake taua:

hoki toku: = 1 ki te n-2 e timata

s: = s + mno * f (he + h * Mu); Hei huihuia {tāpiri i tētahi atu take whakanuia e 4 * y _n 2 ranei * y _n}

ki te (mno = 4) ka mno: = 2 atu mno: = 4; {rerekē tēnei take, me te - ki te mea inaianei ko 4, kua puta ke ki te 2 me te hurihia}

mutu;

simpsonmetod: = s * h / 3; {Whakanuia huringa moni hua e h / 3} muri rite ki tātai

mutunga.

Ko te reira - te mahi i mahi katoa rite ki te tātai. Ki te mea kua kore ngā koe i roto i pehea ki te tono i roto i te tikanga hōtaka matua tauira o Simpson te āwhina koe ki tenei.

Na i muri i te tuhi mahi tuhituhi katoa

Tīmataria te

n: = 3; whakaturia tatou {n}

q: = simpsonmetod (he, b, n); {Mai te tikanga Simpson, ko ki whakatatau te wāhi o te ki te b, i reira ka kia maha ngā kaupae tātai, kia whakarite huringa}

tukurua

q2: = q; {Taahiraa o mua tamau aau}

n: = n + 2;

q: = simpsonmetod (he, b, n); tātai uara {Na} te rite whai

tae noa ki (abs (q-q2) <0.001); {te tika tautuhinga i tuhituhia, na tae noa tae koe te tika hiahiatia, he mea e tika ana ki te faahiti i te taua mahi}

Tenei te he ia - tikanga Simpson. I roto i te meka, kahore faingataa, kei te tino kaika tuhituhia nga mea katoa! Na whakatuwhera koutou Turbo Pascal, me te tīmata te tuhi i te hōtaka.