bca3010 smu bca fall 2016 IIIrd sem solved assignments

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Fall 2016, 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. Find the Taylors Series for 𝑓(𝑥) = 1/𝑥²about 𝑥₀ = −1

Answer:

Solution: We know the Taylor’s series expansion of function at

2. Use the Regula-Falsi method to compute a real root of the equation x³ – 9x + 1 = 0, if the root lies between 2 and 4.

Answer:

Let f(x) = x³ – 9x + 1. Now f(2) = – 9 and f(4) = 29.

Since f(2) and f(4) are of opposite signs, the root of f(x) = 0 lies between 2

and 4.

Take x1 = 2 and x2 = 4.

3. Solve by Gauss elimination method.

2x + y + 4z = 12

4x + 11y – z = 33

8x – 3y + 2z = 20

Answer:

The augmented matrix of the

4. For the approximate value of by simpson’s 1/3^rd rule by dividing  into 6 equal parts

Solution.

Solution: Here

a = 0,

b =

p

,

n = 6,

2

p

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 

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

Solution.

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