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![Page 1: IV NUMERIČKA INTEGRACIJA - poincare.matf.bg.ac.rspoincare.matf.bg.ac.rs/~zstanic/unm/Slajdovi/04. numericka...Neka su Ih i 12h približne vrednosti integrala I izrachmate pomoéu](https://reader036.vdocuments.net/reader036/viewer/2022081802/5ac9c69a7f8b9a51678d7838/html5/thumbnails/1.jpg)
IV NUMERIČKA INTEGRACIJA
0. OPŠTE O NUMERIČKOJ INTEGRACIJI
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Formule (4), (5) se nazivaju Njutn-Kotesove kvadraturne formule.
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Sada ćemo izvesti opšti oblik Njutn-Kotesovih kvadraturnih formula sa ekvidistantno raspoređenim čvorovima.
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2. FORMULA PRAVOUGAONIKA I TRAPEZNA KVADRATURNA FORMULA
Formula pravougaonika dobija se kada se u opštem obliku Njutn-Kotesovih kvadraturnih formula stavi n=0, t0=(a+b)/2. Dobija se
Greška gornje formule ocenjuje se izrazom
Ukoliko u formulama
stavimo n=1, dobijmo se
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Geometrijski smisao...
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x_0
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Prema opštoj formuli za grešku (1.6).
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Kada se u formulama
stavi n=2, dobija se
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Simpsonova kvadraturna formula je tačna za sve polinome trećeg stepena
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Na sličan način se može izvesti Rungeova ocena greške za uopštenu trapeznu formulu. Od ove se razlikuje u imeniocu gde umesto 15 stoji 3.
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Ne predstavlja gornju granicu!
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