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Seat No.: Enrolment
GUJARAT TECHNOLOGICAL UNIVERSITY
MCA SEMESTER II • EXAMINATION SUMMER 2018
Subject Code: 620005 Date: 23-May-2018
Subject Name: Computer Oriented Numerical Methods
Time: 10.30 am to 1.00 pm Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q.1 Find the root of the equation x3 0 using the Bisection method.
Perform iterations until the accuracy till four significant digit.
07
Find the root of the equation x4 +24x -50 correct up to three significant
digits using Birge-Vieta method. Assume the initial value of the root 1.5
07
Q.2 Explain total numerical error. How can one control numerical errors
State Descartes rule of sign. Use it to determine the number of positive
and negative roots of the polynomial equation x4 3x3 2x2 20x 20
07
Use secant method to find a root of the following
equation x3 5x+3 correct up to three decimal places.
07
OR
Use Newton-Raphson method to find a root of the following
equation x3 4x-9 correct up to three decimal places between 2.625 and 3.
07
Q.3 From the following table, find y when x 0.4 using Lagrange's interpolation
formula.
X 0.3 0.5 0.6
y 0.61 0.69 0.72
07
Fit a straight line of the form y a bx, to the following data
x 0.1 0.2 0.3 0.4 0.5 0.6
y 5.1 5.3 5.6 5.7 5.9 6.1
07
OR
Q.3 Compute value of y at x=0.02 using suitable interpolating polynomial
X 0.0 0.1 0.2 0.3 0.4
Y 1.0000 1.1052 1.2214 1.3499 1.4918
07
Fit an exponential curve for the following data:
x 600 500 400 350
y 2 10 26 61
07
Q.4 Compute the second order derivative for the following set of data values at x=3
X 0 1 2 3
1 9 25
07

Evaluate
2 1

2
1
x
e dx

using trapezoidal rule for four intervals.
07
OR
Q.4 The distance covered by a car in a given time is given in the
following table
Time (minutes) 10 12 16 17 22
Distance 12 15 20 22 32
Find speed of the car at t=14 minutes.
07
2

Evaluate
4
2
2
x x dx using Gauss Quadrature formula.
07
Q.5 Solve the following system of simultaneous linear equations using Gauss-
Elimination method:
2x+8y+2z=14
x+6y-z=13
2x-y+2z=5
07
Given 2 dy dx y with y(0)=0,y(0.2)=0.2027,y(0.4)=0.4228,y(0.6)=0.6841.
compute y(0.8) using Milne simpson's Predictor-Corrector method.
07
OR
Q.5 Solve the following system of simultaneous linear equations using Gauss-
Seidel method:
10x+y+2z 44
2x+10y+z 51
x+2y+10z 61
07
Given 2 dy dx y with y(0)=0,y(0.2)=0.2027,y(0.4)=0.4228,y(0.6)=0.6841.
compute y(0.8) using Adam-Bashforth Predictor-Corrector method.
07