# Computer Application in Civil Engineering January 2013

UNIT – I

1.  (a) What is error ? Explain absolute and relative error in detail also explain the meaning of approximations and round of errors in detail.

(b) Write short note on truncation errors.

OR

1. (a) If we want to approximate e10 5 with an error less than 10-12 using the Taylor series for / (*) = ex at 10, at least how many terms are needed.

(b) Explain how truncation errors can be estimated by geometry series.

UNIT – II

(a)  Iterate two times using the Gauss-Seidel method, stating with the initial approximations as Xj=0.3, x2=-0.8 and *3=0.3.

OR

(a) Explain successive substitution method with its derivation and algorithm.

(b) Derive formula for decomposition methods also write down its algorithm.

UNIT – III

(a)  Fit a second degree parabola to the following data :

 x : 1 2 3 4 5 6 7 y : 1.1 1.6 2.7 4.1 5.8 6.9 8.2

(b) Explain various applications of difference relations in the solution of differential equations with an example.

OR

(a)  Given data is

 A 1 1.1 1.2 1.3 1.4 1.5 1.6 B 7.989 8.403 8.781 9.129 9.451 9.75 10.031

(b) Write short note on non-liner Regression analysis.

UNIT – IV

4    (a) Write an algorithm for Simpson’s — rule for a known function.

(b) State the assumptions made and derive the expression for numerical integration using Simpson — rule.

OR

4. (a) Evaluate, by using Newton’s method for integration.

(b) Trapezoidal method, Simpson method and Simpson method.

UNIT – V

5. (a) Give Algorithm and explain Range-Kutta fourth order method for solution of differential equation of first order and first degree.

(b) Derive equations for Numerical solution of ordinary differential equations by Euler method.

OR

5. (a) Derive an equation of ordinary differential equation by predictor – corrector method with its Algorithm.

(b) Apply Predictor corrector method to find >’(0.6) for differential equation Dy= > given >;(°) = °3 >(0.2) = 0.02, >(0.4) = 0.0795.