BCA3010 -COMPUTER ORIENTED NUMERICAL METHODS

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SUMMER 2013, ASSIGNMENT

DRIVE	SUMMER 2015
PROGRAM	BACHELOR OF COMPUTER APPLICATION
SUBJECT CODE & NAME	BCA3010 -COMPUTER ORIENTED NUMERICAL METHODS
SEMESTER	THIRD
CREDITS	4
MAX. MARKS	60
BK ID	B

Answer all questions

Q. 1 Solve the system of equation by matrix inversion method

x +y +z = 1

x +2y + 3z = 6

x + 3y +4z = 6

Solution:-Write the given as a single matrix equation:

1         1  1         x              1

1     2   3         y    =       6

1     3    4        z              6

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

A = I 8  - 6     2 I

  I 6     7     4 I

  I 2     4     3 I

Q. 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: -

y = ax^3 + bx^2 = cx +d.

y(0) = 1 = 0+0+0+d, d = 1

y(1) = 0 = a+b+c+1, a+b+c = -1

y(2) = 1 = 8a + 4b + 2c + 1, 8a+4b + 2c = 0

y(3) = 10 = 27a + 9a + 3c + 1, 27a + 9a + 3c = 9 --à 9a + 3b + c

a + b +c = -1

8a + 4b + 2c = 0

9a + 3b + c = 3

Eq. 1: a – 9a + b – 3b + c – c = -1 -3

-8a -2a = -4

-4a –b = -2

4a +b = 2

Eq.2 : 2 -  2*eq.3: 8a – 18a +4b -6b +2c – 2c = 0-6

Q. 4. Find the approximate value of ò p/2,0 √ cos q dq by Simpson’s 1/3rd rule by dividing [0, p/2] into 6 equal parts.

Solution:- A method for approximating the value of a function near a known value. The method uses the tangent line at the known value of the function to approximate the function's graph. In this method Δx and Δy represent the changes in x and y for the function, and dx and dy represent the changes in x and y for the tangent line.

Q. 5. Use Picard’s method of successive approximations to find y1,y2, y3 to the solution of the initial value problem

Solution:-

Y ‘ = y

Q. 6.  Solve x y + y = 0, y  (1) = 0, y(2) = 1, h = 2/1

Answer : To solve an equation is to find what values (numbers, functions, sets, etc.) fulfill a condition stated in the form of an equation (two expressions related by equality). When searching a solution, one or more free variables are designated as unknowns. A solution is an assignment of expressions to the unknown variables that makes the equality in the equation true. In other words, a solution is an

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