Iyini indlela Simpson, nokuthi ungasebenzisa kanjani ke ngolimi Pascal

Ukuze abale ukubaluleka i ebalulekile, siqala eseduzane, kukhona indlela enhle kakhulu, yaqanjwa kumdlali - indlela Simpson. Washayela parabolas indlela, ngoba usebenzisa ukwakhiwa parabola. Lesi sibalo kusekelwe eduze ngangokunokwenzeka ukuze umsebenzi. Empeleni, indlela indlela yokwakha parabola, okukhomba luqondane ncamashi ne amaphuzu umsebenzi, akunakwenzeka, kanye ebalulekile is yilo. Formula indawo yalo nge futhi b libukeka kanje: 1 / h * (y + 4y _{0 1} + 2y ₂ + 4y ₃ + ... + 4y _n-1 + y _n). Lapha, thina nje ubale y ngamunye kusukela 0 kuya n, lapho n thina ezichaza ngokwethu - kulapho, ngcono, ngoba kulapho-y s, eseduze xaxa ukubaluleka umsebenzi wethu kweqiniso. Mayelana h, bese lesi sinyathelo ibalwa le ndlela elandelayo: (ba) / (n-1).

Okwazekayo, konke ulula, kodwa kuyoba letifanele ekwetfuleni konke lokhu practice. Ukuze program eziningi ayikho indlela engcono ukuxazulula le nkinga, njengoba indlela Simpson - Pascal noma eDelphi. Esimweni esinjalo, kulula kakhulu hhayi kuphela ukuhlola ebalulekile, kodwa futhi ukwakha igrafu umsebenzi ke, ngisho eyakhelwe esishwibweni wakhe. Ngakho, sibheka indlela ungakwazi masinyane kusebenze indlela Simpson ngisho ukuchaza, uma uthanda, ndawo zombili lapha ehlelelwe, bonke nesithakazelo.

Kodwa ngiyakhumbula ukuthi kubukeka kanjani ngaphambi kwalokhu ebalulekile. Lesi sibalo, okuyinto iphahlwe imigqa oqala-eksisi 'X', isb a futhi b.

Ngakho, ukuqala uhlelo udinga ukudala umsebenzi kwemisebenzi integrable (uyixolele tautology), okuyinto umane ukubhala f: = nento esingajulisa uzothola ebalulekile. Lapha, kubalulekile hhayi ukwenza iphutha endleleni angene emcimbini e Pascal. Kodwa-ke udaba olwehlukile. Ikhodi okuholela izobukeka kanje:

umsebenzi f (x: real): yangempela;

Futhi izici umbhalo oyisisekelo

uqale

f: = 25 * ln (x) + isono (10); {Lapha futhi udinga bhala okuqukethwe imisebenzi yayo}

ukuqeda;

Bese ubhala umsebenzi ukusebenzisa indlela Simpson. Qala kuyoba into efana:

umsebenzi simpsonmetod (a, b: yangempela; n: inamba): yangempela;

Ngokulandelayo, simemezela eziguquguqukayo:

var

s: yangempela; {Subtotals (eminye baqonde)}

h: yangempela; {Isinyathelo}

wami: inamba; Vele {esiphikisayo}

MNO: inamba; {} I multipliers olandelayo

Futhi manje, eqinisweni, uhlelo uqobo:

uqale

h: = (ba) / (n-1); {Lindela isinyathelo ngokuvumelana formula standard. Ngezinye izikhathi isinyathelo okulotshwe umsebenzi, kulesi simo, kule formula asisebenzi}

s: = f (b) + f (a); {Sikhishwe kokuqala iphimbo ukubaluleka}

MNO: = 4; {Khumbula ifomula - 1 / h * (y + 4y _{0 1 ...} ukuthi lo 4 lapha nesipelite, isici sesibili kuyinto 2, kodwa okwengeziwe ngale kamuva}

Manje njengoba indlela efanayo eyisisekelo:

yami: = 1 kuya n-2 musa aqale

s: = s + MNO * f (a h + * Mu); Ngamafuphi {wengeze esinye isici iphindwe 4 * y _n noma 2 * y _n}

uma (MNO = 4) bese MNO: = 2 enye MNO: = 4; {Lokhu isici kuyehluka futhi - uma manje 4, washintsha 2 kanye noHezekeli}

ukuqeda;

simpsonmetod: = s * h / 3; Okulandelayo {umjikelezo okuholela isamba iyanda yi h / 3} ngokuvumelana ifomula

ekupheleni.

Yilokho - ukwenza zonke izenzo ngokuvumelana ifomula. Uma ungazange sesizicabangile out indlela ukusebenzisa in the main Uhlelo indlela isibonelo Simpson sika ukukusiza ngalokhu.

Ngakho ngemva kokubhala yonke imisebenzi bhala

Qala

n: = 3; Sigxilisa {n}

q: = simpsonmetod (a, b, n); {Njengoba indlela Simpson kuyinto ukubala ehlangene ukuze b, kuyoba kukhona izinyathelo ezimbalwa ukubala, ngakho uhlele umjikelezo}

uphinda

Q2: = q; {Ngekhanda isinyathelo odlule}

n: = n + 2;

q: = simpsonmetod (a, b, n); {Futhi} Inani ibalwa kanje

kuze (ABS (q-Q2) <0,001); {Ukunemba kulungiselelwa ebhaliwe, ngakho uze ufike ukunemba okunjalo, kubalulekile ukuphinda izenzo efanayo}

Nayi-ke - indlela Simpson. Eqinisweni, akukho nzima, konke okulotshwe ngokushesha okukhulu! Manje vula Turbo yakho Pascal bese uqala ukubhala uhlelo.