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MTH603 - Numerical Analysis Assignment No. 2 Solution and Discussion Spring 2014 of VirtualUniversity (VU) Due Date: July 14, 2014

Assignment # 2 (Lecture# 23 - 28) Of MTH603 (Spring 2014) 

Maximum Marks: 30 
Due Date: 14 July, 2014 



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Question: 1 Marks: 5 + 10 

Using Lagrange’s interpolation formula, find the value of cos
6
  π
    using the following table. 
Also 
estimate the error in the solution. 

x 0 
4
π 
2
π 
y x =cos 1 0.7071 0 



Question: 2 Marks: 2.5 + 2.5 + 5 + 5 

Estimate (2 3. ) d
dx
and (1 3. ) d
dx
, using the following table. 

x 1.3 1.5 1.7 1.9 2.1 2.3 
y 3.753 3.523 3.333 1.9922 1.5442 1.2969

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check this if error then accurate this

SINCE X=2.3 OCCURS AT THE END OF THE TABLE,SO WE WILL USE BACKWARD DIFFERENCE FORMULA for derivatives

The backward difference table for the given data is given below

X

F(x)

Δy

y

y

y

y

1.3

3.753

 

 

 

 

 

1.5

3.523

-0.5

 

 

 

 

1.7

3.333

-0.1900

0.3100

 

 

 

1.9

1.9922

-1.3400

-1.1500

-1.4600

 

 

2.1

1.5442

-0.4480

0.8920

2.0420

3.5020

 

2.3

1.2964

-0.2773

0.1707

-0.7213

-2.7633

-6.2653

NOW FOR  

SINCE 1.3 appear at the beginning of the table so we will use forward difference formula for which table is given below

X

F(x)

Δf(x)

f(x)

f(x)

f(x)

f(x)

1.3

3.753

 

 

 

 

 

1.5

3.523

-0.5

 

 

 

 

1.7

3.333

-0.1900

0.3100

 

 

 

1.9

1.9922

-1.3400

-1.1500

-1.4600

 

 

2.1

1.5442

-0.4480

0.8920

2.0420

3.5020

 

2.3

1.2964

-0.2773

0.1707

-0.7213

-2.7633

-6.2653

 

 

Using the forward difference formula

=

=

==-5.8270


is ka table ghalat hai...........

g 0.04 ki jaga 0.4 likha hua hy

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