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Newton–Cotes formulas, also called the Newton–Cotes quadrature rules
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| bet | 1/3 | | Sana | 18.05.2024 | | Hajmi | 75,25 Kb. | | #240927 |
Bog'liq AL MI|
AXBOROT TEXNOLOGIYALARI VA KOMMUNIKATSYALARINI RIVOJLANTIRISH VAZIRLIGI MUHAMMAD AL-XORAZMIY NOMIDAGI TOSHKENT AXBOROT TEXNOLOGIYALARI UNIVERSITETI ALGORITMLARNI LOYIHALASH FANIDAN
MUSTAQIL ISH
Mavzu:Integrallarni taqribiy hisoblashda Nyuton-Kottes formulalari.G’oyasi va xatolik tartibi.
Guruh:027-21 guruh talabasi
Bajardi:Odiljonov Izzatillo
Tekshirdi:Narmanov O
REJA:
1.Integrallarni taqribiy hisoblash usullari.
2.Nyuton-Kottes formulalari.
3.Nyuton Kottes formulalarining g’oyasi va xatoliklar tartibi.
4.Xulosa.
In numerical analysis, the Newton–Cotes formulas, also called the Newton–Cotes quadrature rules or simply Newton–Cotes rules, are a group of formulas for numerical integration (also called quadrature) based on evaluating the integrand at equally spaced points. They are named after Isaac Newton and Roger Cotes.
Newton–Cotes formulas can be useful if the value of the integrand at equally spaced points is given. If it is possible to change the points at which the integrand is evaluated, then other methods such as Gaussian quadrature and Clenshaw–Curtis quadrature are probably more suitable.
Description[edit]
It is assumed that the value of a function f defined on is known at equally spaced points: . There are two classes of Newton–Cotes quadrature: they are called "closed" when and , i.e. they use the function values at the interval endpoints, and "open" when and , i.e. they do not use the function values at the endpoints. Newton–Cotes formulas using points can be defined (for both classes) as[1]
where
The number h is called step size, are called weights. The weights can be computed as the integral of Lagrange basis polynomials. They depend only on and not on the function f. Let be the interpolation polynomial in the Lagrange form for the given data points , then
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