/*Numerical Integration And Derivation*/

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??? ????????? /Numerical Integration And
Derivation/
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(2)????????????,????? (3)?????????,??????
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5.1 ?????????
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??????????(/Algebraic Precision /)
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5.2 NewtonCotes??
?????????/Integration Formula of Interpolation
Type/
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?n?Lagrange?????
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?? NewtonCotes????
NewtonCotes???????????????
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Cotes??
NewtonCotes??
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????/Trapezoidal Formula /
n1??????
1?????
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Simpson??
n2??????
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Cotes??
n4??????
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?n????, NewtonCotes???????? n1??????
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? Simpson??
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? Cotes??
NewtonCotes???????
?????????,??????????? ?,????????,????????,??? (1)?
??????Runge??
(2)NewtonCotes??????????(ngt7)
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5.3 ??????/Compound Quadrature Formula /
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????Simpson?? /Compound Simpon Formula /
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??Simpson??
??Simpson???????
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??Simpson?????
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???(5)
??Simpson??????
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??Simpson?????
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0 1/8 1/4 3/8
1 0.997398 0.989688 0.976727
1/2 5/8 6/8 7/8 1
0.958851 0.936156 0.908858 0.877193 0.841471
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??????(n8)
??Simpson??(n4)
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(2)??????????,????????????
(3)?????????????,????????
(4)???????????,??????????
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3?????
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?????Simpson???Cotes????????
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??????????????????? Simpson????Cotes????????
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5.4 Romberg???/Romberg Integration Method /
? Romberg????
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Romberg????????????
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Simpson????
Romberg ???
Cotes????
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????3???????????????, ???Romberg????
4??????
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Simpson???
Cotes???
Romberg???
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Romberg????????
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Romberg???
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??Romberg ??????
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5.5 Gauss????/Gauss Quadrature Formula /
?? Gauss???????
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???NewtonCotes???????????????,????????,??????????

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??2n1??????
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2n2????, 2n2??????????
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?? Gauss???????
? Gauss?????????
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?????()??????2n1?????????
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? Gauss????????????
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? Gauss???????
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? Gauss????????
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??Gauss?????()??????2n1??? ???????
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? Gauss????????
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?Weierstrass???
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?? Gauss???????
???????,????n1???????n1? ???????,?????????Gauss?
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????Legendre????Chebyshev?????
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? Gauss-Legendre????
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????2n?
P147 ?5.5.1
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??Gauss-Legendre????
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? Gauss-Chebyshev????
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5.6 ???????? /The Numerical
Solution of Integral Equations /
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??????????Fredholm??????,?? ?????????????
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???????????Fredholm???????
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???Simpson????????(?????)
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0 0.25 0.5 0.75 1
-7.9256 14.5225 -40.6597 -0.4504 31.4884
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5.7 ????/Numerical Derivation /
?????????/ Derivation Formula of Interpolation
Type/


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