He aha ke'ano o Simpson a me pehea e ho'okomo ai ia mea ma ka'ōlelo Pascal

No ka ho'ohālikelike'ana i ke kumu o ka ho'ohui,'oiai paha e pili ana, aia kahi hana maika'i loa i kapa'ia ma hope o kona mea hana, ke'ano Simpson. Ua kapa'ia'o ia ke'ano o ka'ōwili, no ka mea, ho'ohana ia i ke kūkulu'ana i kahi pahu. Ua kūkulu'ia kēia ki'i ma kahi kokoke loa i ka hana. 'O ka'oia'i'o, no ka mea hiki'ole ke kūkulu i kahi pīpōpō e like ana me nā helu o ka hana, e like me nā kiko o ka hana, ua pili ka mea pili. Haʻilula wahi o kona palena me ka a e nānā me keia. 1 / h * (y me + 4y _{0 1} + 2y ₂ + 4y ₃ + ... + 4y _N-1 + y me _N). Maanei, pono mākou e helu i kēlā me kēia y mai 0 a n, kahi i ho'oholo'ia e mākou -'o ka'oi aku,'o ka maika'i, no ka mea,'oi aku ka nui o nā y-s,'o ka pili loa i ka waiwai maoli i loa'a iā mākou. No ka h, ua helu'ia kēia māhele e ke kumuhana penei: (ba) / (n-1).

I ke kumukānāwai, he mea ma'alahi nā mea a pau, akā he mea pono e ho'okō i kēia mau mea a pau. No nā polokalamu polokalamu he nui,'a'ohe ala maika'i e ho'oponopono ai i kahi pilikia e like me ka Simpson-Pascal a i'ole Delphi. Ma kēia wahi, he mea ma'alahi'ole ka helu'ana i ka mea i ho'ohui'ia, akā, no ka kūkulu'ana i kahi pā'ani pākahi a me kahi trapezium i kūkulu'ia no ia. No laila, e'ike mākou pehea e ho'okomo koke ai i ke'ano Simpson a, inā makemake'ia, e wehewehe i kahi pehea a me ka mea i ho'onohonoho'ia, no nā mea a pau i makemake.

Akā, ma mua o ia, e ho'omana'o i ka'ike'ana o ka mea. He ki'i kēia i ho'opa'a'ia e nā laina e ho'omaka ana ma ka axis x,'o ia ho'i, a a me b.

No laila, pono'oe e ho'okumu i kahi hana no ka hana kū'oko'a ('oni no ka tautology) ma ka papahana, kahi āu e pono ai e kākau f: = a me ka mea e loa'a ai iā mākou ka pilina. He mea nui e'ole e hana hewa i ke komo'ana i ka hana ma Pascal. Akā, he'ano ma'amau kēia no ke kama'ilio'ana. 'O ka huahana ho'opuka e nānā i kahi mea e like me kēia:

Nā hana f (x: real):'oia'i'o;

A'o ka mea nui o ka hana

E ho'omaka

F: = 25 * ln (x) + hewa (10); [Pono'oe e kākau i nā mea o kāu hana}

Ho'opau;

A laila, kākau mākou i kahi hana no ka ho'okō'ana i ke'ano Simpson. 'O ka ho'omaka e like me kēia:

'Oihana simpsonmetod (a, b:'oia'i'o; n: mea nui):'oia'i'o;

'O ka hope a'e, e ha'i i nā ho'ololi:

'O Var

S:'oia'i'o; [Ho'oka'awale waena]

H:'oia'i'o; {Step}

'O ka'u: helu helu; [Kikokikona wale nō]

Mno: mea nui; 'O nā mea hua'ōlelo pinepine

A i kēia manawa,'o ia,'o ka polokalamu pono'ī:

E ho'omaka

H: = (ba) / (n-1); [Ke helu nei mākou i ke ka'ina ma ke'ano ma'amau. I kekahi manawa ua kākau'ia kekahi ka'ina i loko o ka hana, i'ole ke kumu e pili'ole ai kēia kulekele}

S: = f (b) + f (a); E ho'onoho i kahi ho'onohonoho mua.

Mno: = 4; , E hoomanao i ka haʻilula - 1 / h * (y me + 4y _{0 1 ...} i keia 4ʻaneʻi a me ka pela, i ka lua o ka ololi o 2, akā, nui ma keia hope}

I kēia'ano kumuhana like'ole:

No ka ho'omaka'ana o ka'u: = 1 i n-2

S: = m + m (a + h * mu); E helu, hoʻohui kekahi ololi hoonuiia e 4 * y me _N a 2 * y me _N}

Inā (mno = 4) a laila mno: = 2'oko'a mno: = 4; Eia ke ho'ololi'ana o nā huahelu - inā he manawa 4 kēia, a laila e ho'ololi i ka 2 a'o ka hakahaka)

Ho'opau;

Simpsonmetod: = s + h / 3; A laila ua ho'onui'ia ka huina huahelu e ka h / 3 e like me ke kumuhana.

Ho'opau.

'O ke'ano - hana mākou i nā hana a pau e like me ke kumu. Inā'a'ole'oe i ho'oholo i ke'ano o ka ho'ohui'ana i ke'ano Simpson i ka papahana nui, e kōkua ana kēia hi'ohi'ona iā'oe.

No laila ma hope o ka kākau'ana i nā hana a mākou e kākau ai

E ho'omaka

N: = 3; Nānā

Q: = simpsonmetod (a, b, n); [Mai ke kumu o Simpson e helu i ka ho'ohui mai ka a a b, hiki ke helu'ia nā ku'ina, pēlā mākou e ho'onohonoho i ke kele}

E hana hou

Q2: = q; [Ua ho'omana'o'ia ka hana mua]

N: = n + 2;

Q: = simpsonmetod (a, b, n); [A helu'ia ke koho hope loa]

Kuhi (q-q2) <0.001); Ua kākau'ia ka pololei o ka hana, pēlā a hiki i ka holo'ana o ka pololei pololei, pono'oe e hana i nā hana ho'okahi.

'O ia'o ia -'o ke'ano o Simpson. 'O ka'oia'i'o,'a'ohe mea pa'akikī, ua kākau wikiwiki'ia nā mea a pau! E wehe i kāu Turbo Pascal a ho'omaka e kākau i ka papahana.