Gaussian Quadrature Formula

Gaussian Quadrature Formula-BY GROUP NO. 9-MECHANICAL DEPARTMENT-4 T H SEMESTER-COMPLEX VARIABLES AND NUMERICAL METHODS(2141905)

Gaussian Quadrature Formula

b

a

1

1-

f(x)dx. f(t)dt to

integral thefrom dtransforme

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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!