Gaussian Quadrature Formulas, which are simple and will help learners learn about Gauss's One, Two and Three Point Formulas, I have also included sums so that learning can be easy and the method can be understood.
2. Gaussian Quadrature Formula
b
a
1
1-
f(x)dx.f(t)dt to
integralthefromdtransforme
becan;
2
1
2
1
t
ofnnsformatiolinear traThe
abxab
3. Gaussian One Point Formula
1. The Gaussian One Point Formula to convert an integral into its
linear transform is given by
1
1
)0(2)( fdxxf
4. Gaussian Two Point Formula
2. The Gaussian Two Point Formula to convert an integral into its
linear transform is given by
3
1
3
1
)(
1
1
ffdxxf
5. Gaussian Three Point Formula
3. The Gaussian Three Point Formula to convert an integral into
its linear transform is given by
1
1
5
3
5
3
9
5
)0(
9
8
)( fffdxxf
6. Example of Gaussian Quadrature
Formula
formula.pointthreeand
pointtwopoint,oneby
x1
dx
Evaluate
1
1
2
2
1
1
x
Here f(x)
7. Example of Gaussian Quadrature
Formula
mulaPoint Forussian Oneound by Gawhich is f
2f(x)dx
(0)1
1
2
2f(0)f(x)dx
1
1
2
1
1
8. Example of Gaussian Quadrature
Formula
1
1
50.1)( dxxf
1.50
0.750.75
f(0.57735)0.57735)f(
3
1
f
3
1
ff(x)dx
t Formula,n Two PoinBy Gaussia
1
1
10. Example of Gaussian Quadrature
Formula
1.305f(x)dx
1.305
9
11.75
9
3.75
9
8
1
-1
11. Example of Gaussian Quadrature
Formula
Formula.hree Pointdx with T2xxEvaluate
4
2
2
3tx
2)(4
2
1
t24
2
1
x
42, ba
ab
2
1
tab
2
1
Here x