BCA 12 Computer Oriented Numerical Methods - BCASPOT ASSIGNMENT (CY-2013 AY 2013-2014)

Bachelor of Computer Applications

Second Year

Course Code : BCA-12

Course Title : Computer Oriented Numerical Methods

(Total Marks=25)

Part- A- Short Answer Questions

Answer all questions                                                                      (3 X 5 = 15 Marks)

1)    The equation 2x3+5x2+5x+3=0 has a root in the interval [-2,-1] Starting with X0=-2.0 and x1=-1.0 as initial approximations, perform three iteration of the Regula-falsi method.

Answer:

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2)    Find the Positive root of x-cosx=0 by bisection method.

Answer:

Solution :

Let f(x) = x – cos x

f(0) = 0 - cos (0) = 0 -1 = -1 = -ve

f(0.5) = 0.5 – cos (0.5) = -0.37758 = -ve

f(1) = 1 – cos (1) = 0.42970 = +ve

So root lies between 0.5 and 1

Let xo = (0.5 +1) /2 as initial root and proceed.

f(0.75) = 0.75 – cos (0.75) = 0.018311 = +ve

So root lies between 0.5 and 0.75

x1 = (0.5 +0.75) /2 =0.625

f(0.625) = 0.625 – cos (0.625) = - 0.18596

So root lies between 0.625 and 0.750

x2 = (0.625 +0.750) /2 = 0.6875

f(0.6875) = - 0.085335

So root lies between 0.6875 and 0.750

x3 = (0.6875 +0.750) /2 = 0.71875

f(0.71875) = 0.71875-cos(0.71875) = - 0.033879

So root lies between 0.71875 and 0.750

x4 = (0.71875 +0.750) /2 = 0.73438

f(0.73438) = -0.0078664 = - ve

So root lies between 0.73438 and 0.750

x5 = 0.742190

f(0.742190) = 0.0051999 = + ve

x6 = (0.73438 +0.742190) /2 = 0.73829

f(0.73829) = -0.0013305

So root lies between 0.73829 and 0.74219

x7 = (0.73829+0.74219) = 0.7402

f(0.7402) = 0.7402-cos(0.7402) = 0.0018663

So root lies between 0.73829 and 0.7402

x8 = 0.73925

f(0.73925) = 0.00027593

x9 = 0.7388

The root is 0.7388.

3)    A table of x versus f(x) is given below. Using Lagrange’s interpolation formula find the value of f(x) at x=4

X	1.5	3	6
F(X)	-0.25	2	20

Solution:

The Lagrange formula for the above table is

Part- B- Long Answer Question

Answer the following question                                                     (1 X 10 = 10 Marks)

1)      Apply the fourth order Runge-Kutta Method to find Y(0.2) given that Y’=X+Y, Y(0)=1.

Answer:  

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