bca3010 smu bca summer 2014 III sem assignment

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Summer 2014, ASS IGNMENT

PROGRAM-BCA(REVISED FALL 2012)

SEMESTER-3

SUBJECT CODE & NAME BCA3010 -COMPUTER ORIENTED NUMERICAL METHODS

CREDIT-4

BK ID-B1643

MAX. MARKS-60

Q1. Solve the system of equation by matrix inversion method

x +y +z = 1

x +2y + 3z = 6

x + 3y +4z = 6 

Answer.

The given equation can be written as

AX = B

ð X = A^-1B                           …(*)

Where A =

2. Find all eigen values and the corresponding eigen vectors of the matrix

 

Solution.

The characteristic equation of A is

3. Find the cubic polynomial which takes the following values y(0) = 1,  y(1) =  0,  y(2) = 1 and  y(3)  =  10. Hence or otherwise, obtain y (0.5). 

Solution.

Solution: Here  x0  =  0,  x1 =

1,

x2 =  2,  x3 =

3

4.

Solution.

Solution: Here

a = 0,

b =

p

,

n = 6,

2

Q5. Use Picard’s method of successive approximations to find y1,y2, y3 to the  solution of the initial value problem 𝑦′ = 𝑑𝑦/𝑑𝑥= 𝑦,  given that y =2 for  x = 0. Use y3 to estimate the value of y (0.8).

Solution.

  

Solution: On  comparing    to eq(1) , we get    and y0=2, x0=0

Q6.  Solve x  y”+ y = 0, y ‘(1) = 0, y(2) = 1, h = ½  10

Solution.

x0	= 1,	x1 = 1.5,	x2 = 2
y0	= y(x0) = y(1) = ?
y1= y(x1) = y(1.5) = ?

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