The I-ApproximateInt(f(x), x = a.. b, indlela = simpson[3/8], opts) umyalo olinganiselwe okubalulekile kokuthi f(x) ukusuka ku-a ukuya ku-b ngokusebenzisa umthetho ka-Simpson 3/8. Lo mthetho waziwa nangokuthi umthetho kaNewton's 3/8.
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f (x) | - | isisho se-algebraic ku-variable 'x' |
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a,b | - | izinkulumo ze-algebraic; cacisa isikhawu |
Ngokufanayo, Uyini umthetho kaSimpson 1/3rd? Ekuhlaziyeni izinombolo, umthetho kaSimpson 1/3 uthi indlela yokulinganisa izinombolo zokuhlanganisa okuqondile. Ngokucacile, ukulinganisa okulandelayo: Kumthetho ka-Simpson 1/3, sisebenzisa ama-parabola ukulinganisa ingxenye ngayinye yejika.Siyahlukanisa. indawo ibe n izingxenye ezilinganayo zobubanzi Δx.
Uyini umehluko phakathi komthetho kaSimpson 1/3 kanye no-3/8? I-Simpson's Umthetho we-3/8 ifana nomthetho kaSimpson's 1/3, umehluko kuphela ukuthi, kumthetho we-3/8, i-interpolant iyi-cubic polynomial. Nakuba umthetho we-3/8 usebenzisa inani elingaphezulu lomsebenzi, cishe unembile ngokuphindwe kabili njengomthetho we-1/3.
Uyini umthetho we-Weddle? Umthetho Weddle's indlela yokuhlanganisa, ifomula ye-Newton-Cotes ene-N=6. ISINGENISO: Ukuhlanganiswa kwezinombolo kuyinqubo yokwenza ikhompuyutha inani lokubalulekile okuqondile kusuka kusethi yamanani ezinombolo we-ingrand. Inqubo kwesinye isikhathi ibizwa nge-mechanical quadrature.
Okwesibili Uma sisebenzisa umthetho weSimpson S 3 8 inani lezikhawu uN kumele libe? OkwaSimpsons (3/8)th umthetho ozosebenza, N kumele kube okuningi kwe-3.
Uwusebenzisa kanjani umthetho we-Simpsons 1/3?
ke Yini u-N ekubuseni kukaSimpson? Imithetho kaSimpson. Ikhasi 1. I-Simpsons Rule. Le ndlela ivame ukuveza imiphumela enembe kakhulu kunomthetho we-trapezoidal. Futhi sihlukanisa indawo engaphansi kwejika ibe n izingxenye ezilinganayo, kodwa kulo mthetho n kumelwe kube inombolo elinganayo ngoba silinganisela izindawo zezifunda zobubanzi obungu-2Δx.
Ingabe umthetho kaSimpson uhlale unembe kakhudlwana? Isingeniso Sezindlela Zezinombolo
Umthetho kaSimpson uyindlela yokuhlanganisa izinombolo okuyi-a okuhle kunembe kakhulu kunomthetho weTrapezoidal, futhi kufanele isetshenziswe njalo ngaphambi kokuthi uzame noma yini ejabulisa kakhulu.
Uwusebenzisa kanjani umthetho we-Simpsons 1/3?
Iluphi uhlelo oluphakeme kakhulu lwe-polynomial oluvumela umthetho we-Simpson 1/3 ukuthi uthole inani eliqondile lokuhlanganisa? Uhlelo oluphakeme kakhulu lwe-polynomial integrand lapho umthetho ka-Simpson 1/3 wokuhlanganisa unembile.
1) | yesibili |
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2) | kuqala |
3) | owesine |
4) | wesithathu |
5) | null |
Uwukhumbula kanjani umthetho we-Weddles?
Ithini ifomula yendlela kaNewton Raphson? Indlela ye-Newton-Raphson (eyaziwa nangokuthi indlela ka-Newton) iyindlela yokuthola ngokushesha ukuqagela okuhle kwempande yomsebenzi onenani langempela. f(x) = 0 f(x) = 0 f(x)=0. Isebenzisa umbono wokuthi umsebenzi oqhubekayo nohlukanisekayo ungalinganiswa ngomugqa oqondile we-tangent kuwo.
Ithini ifomula yomthetho we-trapezoidal?
Umthetho weTrapezoidal
T n = 1 2 Δ x ( f ( x 0 ) + 2 f ( x 1) + 2 f ( x 2 ) + ⋯ + 2 f ( xn − 1 ) + f ( xn ) ) .
Ingabe umthetho kaSimpson unikeza umphumela oqondile?
Njengoba isebenzisa ama-polynomials angama-quadratic ukulinganisa imisebenzi, umthetho kaSimpson empeleni unikeza imiphumela eqondile. lapho ukulinganisa okuhlanganisiwe kwama-polynomials kufika ku-cubic degree.
Uyithola kanjani i-K emthethweni we-Simpsons?
Uyini umthetho we-M ku-Simpsons?
Uyithola kanjani i-h kumthetho we-Simpsons?
Kulo mthetho, u-N uyinombolo elinganayo futhi h = (b – a) / N. Amanani angu-y umsebenzi ohlolwayo ngamavelu ahlukaniswe ngokulinganayo ka-x phakathi kuka-a no-b.
Ingabe umthetho kaSimpson unembe kakhulu kune-midpoint? Empeleni, i-Midpoint ingafinyelela ukunemba kwe-Simpsons enkulu kakhulu n. Futhi, ngithole ukuthi iphutha kuTrapezoidal cishe liphindwe kabili iphutha ku-Midpoint, bur kwelinye icala. Enye into ethokozisayo nge-Simpsons ukuthi ukunemba kwayo kuthuthukisa kakhulu ngaphezu kwe-n.
Iyiphi engcono i-trapezoidal noma i-Simpsons?
In trapezoidal sithatha zonke izikhawu njengoba zinjalo . Ku-simpson siphinde siyihlukanise ibe izingxenye ezi-2 bese sisebenzisa ifomula. Ngakho-ke iSimpson inembe kakhulu.
Liyini iphutha emthethweni kaSimpson? Iphutha Liboshelwe Kumthetho KaSimpson: Ake sithi |f(IV )(x)| ≤ K kokunye k ∈ R lapho. a ≤ x ≤ b. Bese. |ES| ≤ k (b − a)5 180n4 Ngisebenzise uphawu ES ukukhombisa iphutha eliboshelwe kumthetho kaSimpson, ET iphutha eliboshelwe kuMthetho weTrapezoid, nokunye.
Siyini isiphindaphinda somthetho wesithathu kaSimpson?
Sinikezwa ama-half-ordinates angu-6 futhi angu-6 alinganayo. Ngakho-ke, asikwazi ukusebenzisa uMthetho Wokuqala kaSimpson.
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Isibonelo sokuqala: Thola indawo yomumo olandelayo usebenzisa uMthetho kaSimpson:
Amakhompiyutha hafu (1) | Ukuphindaphinda kukaSimpson (2) | Umsebenzi Wendawo (3)=(1)x(2) |
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3.5 | 3 | 10.5 |
4.5 | 3 | 13.5 |
5.0 | 1 | 5.0 |
(ingqikithi) Σ 2 | 31.5 |
Ithini ifomula yephutha yomthetho kaSimpson? Njengoba nje umthetho we-trapezoidal uyisilinganiso semithetho yesandla sobunxele nesandla sokudla yokulinganisa okuhlanganisiwe okuqondile, umthetho ka-Simpson ungase utholwe kusukela ku-midpoint kanye nemithetho ye-trapezoidal ngokusebenzisa isilinganiso esinesisindo. Kungaboniswa lokho S2n=(23)Mn+(13)Tn. Iphutha ku-Sn≤M(b−a)5180n4.
Kungani umthetho kaSimpson unikeza umphumela oqondile?
Njengoba isebenzisa ama-polynomials angama-quadratic ukulinganisa imisebenzi, umthetho kaSimpson empeleni unikeza imiphumela eqondile. lapho ukulinganisa okuhlanganisiwe kwama-polynomials kufika ku-cubic degree.
Ithini i-oda lephutha emthethweni we-Simpson? okuwumthetho ojwayelekile kaSimpson. Njengoba ukulinganisa komsebenzi kuyi-quadratic, i-oda eliphakeme kunefomu lomugqa, isilinganiso sephutha somthetho ka-Simpson siwukuthi O(h4) noma O(h4f‴) ukucacisa kabanzi.