Gujarat Technological University 2010 M.C.A Computer Oriented Numerical Methods Remedial ember- - Question Paper

Seat No.    Enrolment N.5o.

GUJARAT TECHNOLOGICAL UNIVERSITY

MCA. Sem-II Remedial Examination December 2010

Subject code: 620005

Subject Name: Computer Oriented Numerical Methods Date: 20 /12 /2010    Time: 10.30 am - 01.00 pm

Total Marks: 70

Instructions:

1.    Attempt all questions.

2.    Make suitable assumptions wherever necessary.

3.    Figures to the right indicate full marks.

4.    Assume data where ever necessary.

Q.1 (a) Describe the Newton-Raphson method and derive its formula analytically.One of 07 the root of the equation sin x - x - 2 =0 lies near x=2.5.Find the root with tolerance

0.001.

2x + y + z =10 3x +2y+3z=18 x + 4y +9z=16

Q.2 (a) Discuss different type of difference table in detail with an assumed suitable 07 example.

(b) Derive the formula to find the root using Bisection method also write algorithm for 07 it.

OR

(b) Write a well commented program for Secant method. Also explain it in detail.

Given a function in t he form of a table as x 2.0 3.0 4.0 Y(x) 6.6 9.2 8.6

Interpolate the value if y(x) using Langrangian polynomial at a.    x = 2.8 b.    x = 3.1 Give the table of values for function as

x:	1.0	1.5	2.0	2.5	3.0	3.5
y:	6.2	7.5	9.0	10.00	11.5	12.0

Determine both the regression lines and also prove that the intersect at (x/n,y/n)

OR

Q.3 (a) Given the following data find the cubic spline equations for the 4 intervals

x 1 2 3 4 5 F(x) 6 -3 6 2 -6

Find the value of f(x) at x = 3.8 (b) From the Taylor series for y(x) ,find y(0.1) correct to four decimal places if y(x) satisfies : yx-yand y(0)=l

Q.4 (a)

Evaluate    using Trapezoidal and Simpsons l/3^rd rule with six

intervals.

(b) Find the solution of the following differential equation = x² + yusing Runge - 0?

fxJE

Kutta second order method for x=0.1 and 0.2 .Given that y = 1 when x = 0.

OR

Find the eigen value of the matrix    07

12 3 A=2 3 1 5 16

Give =l/(x+y) ,y(0)=2,y(0.2)=2.0933,y(0.4)=2.1755,y(0.6)=2.2493.Find y(0.8) 07 di

using Milnes Predictor Corrector formula.

Q.5 (a) Write a well commented program for Gauss - elimination method.    07

28x + 4y - z = 32 x + 3y +10z = 24 2x + 17y + 4z= 35

OR

Q.5 (a) Discuss different types of errors and error propagation in detai; with example    07

(b) Write an algorithm for false position method and explain the method in detail.    07

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Attachment: gujarat-technological-university-2010-m-c-a--53287-1.pdf

Earning:   Approval pending.