Discuss the various sources of errors in numerical methods.

Explain 'significant digits' and 'round off error'.

2. What is the importance of numerical methods in Civil Engineering? Explain with the help of an example.

3. Find a real root of the equation x^3 -2x correct to three decimal places, using

Bisection Method,

Method of False Position.

Use Gauss Elimination Method to solve the equations, 2x y+Z 3x 2y 3z =18 and x 4y 9z =16.

Determine if the following system of equations is well-defined or ill-defined:

2x+y=2 2x 1·01y 2·01

Using Newton's Interpolation formulae, find the cubic polynomial which takes the following values:

24; 120, y 336 and y 720.

Given the values:

x 0 n/4 n/2
y=sin x 0 0.70711 1.0

Use Lagrange's Interpolation formula to find the value of sin

6. Given the following values, find X (correct to two decimal places) for which Y is maximum and also find this value of Y.

X 1·2 1·3 1·4 1·5 1·6
Y 0·9320 0·9636 0·9855 0·9975 0·9996

7. Explain the following:

Simpson's Rule

Unimodal Function

8. Given the differential equation y" with the conditions y 1 and use Taylor's series method to determine the value of y (0·1).

9. What are the difficulties in non-linear programming problems?

10. Explain one-dimensional minimization methods.