gaussian quadrature formula
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Gaussian Quadrature Formula-BY GROUP NO. 9-MECHANICAL DEPARTMENT-4 T H SEMESTER-COMPLEX VARIABLES AND NUMERICAL METHODS(2141905)
Gaussian Quadrature Formula
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a
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1-
f(x)dx. f(t)dt to
integral thefrom dtransforme
becan ;21
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ofn nsformatiolinear tra The
abxab
Gaussian One Point Formula1. The Gaussian One Point Formula to convert an integral
into its linear transform is given by
1
1
)0(2)( fdxxf
Gaussian Two Point Formula2. The Gaussian Two Point Formula to convert an integral
into its linear transform is given by
3
13
1)(1
1
ffdxxf
Gaussian Three Point Formula3. The Gaussian Three Point Formula to convert an integral
into its linear transform is given by
1
1 53
53
95)0(
98)( fffdxxf
Example of Gaussian Quadrature Formula
formula.point threeand
point twopoint, oneby x1
dx Evaluate1
12
211x
Here f(x)
Example of Gaussian Quadrature Formula
mula Point Forussian Oneound by Gawhich is f
2f(x)dx
(0)112
2f(0)f(x)dx
1
1
2
1
1
Example of Gaussian Quadrature Formula
1
1
50.1)( dxxf
1.50 0.750.75
f(0.57735)0.57735)f(
31f
31ff(x)dx
t Formula,n Two PoinBy Gaussia1
1
Example of Gaussian Quadrature Formula
0.7595
98
0.3750.375951
98f(x)dxNow,
0.375530.375, f
53-1, ff(0)
53f
53f
95f(0)
98f(x)dx
a,int Formuln Three PoBy Gaussia
1
-1
1
1
Example of Gaussian Quadrature Formula
1.305f(x)dx
1.305 9
11.75
93.75
98
1
-1
Example of Gaussian Quadrature Formula
Formula.hree Point dx with T2xxEvaluate 4
2
2
3tx
2)(421t24
21x
42, ba
ab21tab
21Here x
Example of Gaussian Quadrature Formula
dt158ttdx2xx
158tt
3t23t2xx
3txdt f(t), dxf(x)1t4 x
1t2when x
1
1
24
2
2
2
22
Example of Gaussian Quadrature Formula
31.29515
98
21.7979.4039515
98f(t)dt
21.797539.403, f
5315, ff(0)
53f
53f
950f
98f(t)dt
a,int Formuln Three PoBy Gaussia
1
1
1
1
Example of Gaussian Quadrature Formula
sum. the given evaluatedFormula we Pointsian Threese of Gauswith the uTherefore
30.667dx2xx
30.667 9
276
9156
9120
4
2
2
Thank You!