Description

SESSION	NOVEMBER 2024
PROGRAM	BACHELOR OF COMPUTER APPLICATIONS (BCA)
SEMESTER	III
COURSE CODE & NAME	DCA2101 COMPUTER ORIENTED NUMERICAL METHODS

 

 

SET-I

 

 

Q1.

Show that: (a)
(b)

Ans 1.

(a)

Proof:

1. Using the definitions of finite difference operators:

1. Midpoint operator
2. Substituting:

Its Half solved only

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Q2.

Find Lagrange’s interpolation polynomial fitting the points:

Hence find .

Ans 2.

Step 1: Lagrange’s Interpolation Polynomial

The Lagrange interpolation formula is:

where  is given by:

 

Q.3.

Evaluate , given the following table of values:

Ans 3.

We use Newton’s Divided Difference Interpolation formula to evaluate .

Step 1: Divided Difference Table

1. Construct the divided difference table:
   • , and so on.

Q4.

Find the equation of the best-fitting straight line for the data:

Ans 4.

We use the method of least squares to find the equation of the best-fitting straight line:

Step 1: Formulas

1. Slope ():
2. Intercept ():

Q 5.

For what values of  and  does the following system of equations have:

1. A unique solution
2. An infinite number of solutions
3. No solution

Given system:

 

Ans 5.

The general system of equations can be written in matrix form:

where

Q6.

Find the solution for  using an interval length of  with Euler’s method to solve:

 

Ans 6.

Step 1: Euler’s Method Formula

Euler’s method is given by:

where .

Given:

• Initial condition: