Yintoni na indlela Simpson, kunye nokuphumeza indlela ngolwimi Pascal

Ukubala ixabiso kokunikeza, nangona ilingane, kukho indlela elihle, ogama emva kumdlali - indlela Simpson. Ezi wazibizayo parabolas indlela, kuba isebenzisa ukwakhiwa parabola. Eli nani isekelwe abe kufutshane kangangoko kunokwenzeka ukuba umsebenzi. Eneneni, indlela yokwakha indlela parabola, nto leyo eyalatha idibana kanye kunye manqaku kulo msebenzi, oko akunakwenzeka, kwaye ephambili ke yilo. Formula indawo imida yayo kunye kunye b sijongeka njengoku: 1 / h * (y + 4y _{0 1} + 2y ₂ + 4y ₃ + ... + 4y _n-1 + y _n). Apha, kufuneka nje ukuba ukubala y ngamnye ukususela 0 ukuya n, apho n ezichaza ngokwethu - kokukhona, bhetele, ngenxa yokuba i ngakumbi y-s, i eyiyona ngakumbi inyaniso yexabiso umsebenzi wethu. Malunga h, yaye ngoko eli nyathelo ibalwa yi le ndlela ilandelayo: (BA) / (n-1).

Ngethiyori, yonke into ilula, kodwa kuya kuba yimfuneko ukuphumeza konke oku xa befundisa. Kuba badwelisi benkqubo ezininzi akukho ndlela engcono ukusombulula le ngxaki, ibe indlela Simpson - Pascal okanye Ugcino. Kule meko, kulula kakhulu nje kuphela ukuvavanya efunekayo, kodwa ukwakha igrafu umsebenzi kuyo, wazakhela neemvumi yakhe. Ngoko ke, sijonga indlela ungenza ngokukhawuleza ukusebenzisa indlela Simpson kwaye bacacise, ukuba oyifunayo, kokubini apha kwaye olulungelelanisiweyo, bonke abo banomdla.

Kodwa khumbula oko kukhangeleka ngathi phambi kwale ebalulekile. Eli nani, nto leyo ngumda imigca ukuqala axis 'X', ngamanye a kunye b.

Ngoko ke, ukuqala inkqubo ufuna ukwenza umsebenzi kwimisebenzi integrable (ungayixoleli tautology), apho kufuneka nje ukuba ubhale f a: = kunye nento apho siya kufumana ebalulekile. Apha, kubalulekile ukuba iceba ngokungena umsebenzi Pascal. Kodwa ibali eyahlukileyo. Ikhowudi sisiphumo kukhangeleka ngolu hlobo:

umsebenzi f (x: wokwenene): lenene;

Kwaye ke iimpawu ezingundoqo umbhalo

uqale

f: = 25 * ln (x) + nesono (10); {Apha kwaye kufuneka ubhale imixholo imisebenzi yayo}

iphele;

Emva koko bhala umsebenzi ukuphumeza indlela Simpson. Qala iya kuba yinto efana:

umsebenzi simpsonmetod (a, b: lenene; n: elipheleleyo): real;

Okulandelayo, sivakalisa eziguquguqukayo:

var

s: real; {Subtotals (eminye)}

h: real; {Step}

wam: elipheleleyo; Nje {counter}

mno: elipheleleyo; {} I multipliers elandelayo

Kwaye ngoku, enyanisweni, inkqubo ngokwayo:

uqale

h: = (BA) / (n-1); {Lindela inyathelo njengoko kwifomula yomgangatho. Maxa wambi inyathelo kubhaliweyo msebenzi, kulo mzekelo, awusebenzi le formula}

s: = f (b) + f (a); {Elinikiweyo pitch lokuqala}

mno: = 4; {Khumbula ifomula - 1 / h * (y + 4y _{0 1 ...} ukuba le-4 apha nespelete, i inkalo yesibini ngu 2, kodwa ngaphezulu kule kamva}

Ngoku indlela efanayo esisiseko:

ngenxa yam: = 1 ukuya n-2 siqale ntoni

s: = s + mno * f (a + h * Mu); Ngamafuphi {yongeza enye inkalo iphinda phindiweyo ngo-4 * y _n okanye 2 * y _n}

ukuba (mno = 4) ngoko mno: = 2 enye mno: = 4; {Lo mba ziyohluka yaye - ukuba ngoku ngu-4, kutshintshwe 2 and vice versa}

iphele;

simpsonmetod: = s * h / 3; Okulandelayo {Umjikelo leyo mali lithi liphindaphindwe h / 3} ngokwe formula

ekupheleni.

Yiloo nto - ukwenza onke amanyathelo ngokomgaqo wokubala. Ukuba siluqondile indlela isicelo kule ndlela engundoqo lwenkqubo ukunceda umzekelo Simpson xa wena lo.

Ngoko emva kokubhala yonke imisebenzi bhala

Qala

n: = 3; Sakha {n}

q: = simpsonmetod (a, b, n); {Ekubeni indlela Simpson kukuba ukubala ebalulekileyo ukuze b, apho kuya kubakho amanyathelo zokubala ezininzi, ngoko amalungiselelo umjikelo}

phinda

q2: = q; {Ezinkqayiweyo kwenyathelo elidlulileyo}

n: = n + 2;

q: = simpsonmetod (a, b, n); {Kwaye} ixabiso ibalwa ngolu hlobo lulandelayo

de (ABS (q-q2) <0.001); {Ukuchaneka sicwangciso kubhaliwe kwathiwa, ukuze ude ufike nokuchaneka efunekayo, kuyimfuneko ukuba ukuphinda izenzo efanayo}

Nali ke - indlela Simpson. Enyanisweni, akukho lula, yonke into ebhalwe ngokukhawuleza kakhulu! Ngoku vula yakho Turbo UPascal kwaye uqale ukubhala le program.