# Computer Application in Civil Engineering Feb 2011

Unit-I

1.a) Find the roots of equation x3 – x – 4 = 0 correct to three decimal places using Newton-Rap son Method.

b) Write the algorithm for finding, roots of a non linear equation using Bisection Method.

OR

a) F ind the truncation error for e x at x — and x = – when we use

i) First three terms

ii) First four terms.

b) Find the real root of / (jc) = x3 – 2x – 5 = 0

by Bisection Method.

Unit -II

2. a) Solve the following system of equations by Gauss-Seidal Method

27 x + 6y – z = 85 6jc+ 15y + 2z = 12 x +y + 54z =110

b) Write the algorithms for solving the Linear simultaneous equations using triangularizing method.

OR

(a)What do you mean by Linear independent simultaneous equations?

(b) Solve the following equations:

x + 2y + 3z = 1 2x + 3y + 2z = 2 3x + 3y + 4z = 1 by Gauss Elimination Method.

Unit-III

(a)Write a short note on “Regression Analysis”.

(b)Fit a second degree parabola to the following data taking x as the independent variable.

 a; : l 2 3 4 5 6 7 8 9 y‘ 2 6 7 8 10 11 11 10 9

OR

(a)Write a short note on “Numerical Analysis.

(b)The ordinates of the normal curve are given by the following table.

 x: 0 0.2 0.4 0.6 0.8 v: j • 0.3989 0.391 0.3683 0.3332 0.2897

Evaluate

(i) y (0-25)               (ii)   y (0.62)

Unit-IV

4 (a)Compute the values of by the

i)       Trapezoidal rule

ii)      Simpson’s ~ rule and compare your result with the true value.

(b)What is the use of “Numerical Integration” to find area of a curve.

OR

a) Evaluate by Simpson’s rule with six intervals.

b) A curve is drawn to pass through the points given by the following table

 x: 1 1.5 2 2.5 3 3.5 4 y’ 2 2.4 2.7 2.8 3 2.6 2.1

Estimate the area bounded by the curve, x – axis and the lines x = 1 and x = 4.

Unit-V

5. a) Use Euler’s modified method with one step to obtain the value ofy at x = 0.1 when ^j-=x2 +y with x = 0, y = 0.94.

b) Explain any one method used for numerical solution of partial differential equation.

OR

Use Runge-Kutta fourth order method to solve £:=-2V with x0 = 00= 1