Final Examination 2009 2

Sulaimani University College of Sciences Physics Department

Final Examination 2008-2009 Second trial

Numerical Analysis Third Stage Time: 3 hours

Q1/ (a) What is the sufficient condition for convergence in the iteration method. (b) Describe the type of convergence and divergence by using figure method. (c) Write the advantage and disadvantage of Newton-Raphson method. (7 mark)

3.5,2.5 , with 0.01 Q2/ (a) Solve the non-linear system by iterative method at , 3 0 5 1 0 2 (b) Write down the central difference interpolation formula associated with the Gauss forward and Gauss backward schemes, and point the appropriate situation of using each of them. (7 mark) / Q3/ Let Construct the divided difference table to find the Newton polynomial based on: 1.1, 2, 3.5, 5, 7.1

(6 mark)

Q4/ The kinematic viscosity of water varies with temperature as shown in the table. Determine the cubic that best fits the data, and use it to compute at 30 , 60 . 0 21 38 55 71 88 1.79 1.13 0.70 0.52 0.33 0.32 10 / (6 mark)

Q5/ Show how Romberg increase the order of error associated with Trapezium rule from Construct a table of Romberg method.

to

. (6 mark)

Q6/ The distance

traveled by an object is given in the table following: 8 9 10 11 12 60.1 67.2 73.7 80.3 87.1 (a) Find the velocity 10 by numerical differentiation. (b) Compare your answer with 7 10 / (6 mark)

Q7/ Find the power series solution of the initial value problem about using the initial condition 0 4.

0 of the differential equation: (6 mark)

Q8/ Consider a typical steady state flow problem 0 , let a thin steel plate having of 10 , and the other edges are held at 0 as a rectangular, let one edge of the 10 at 140 is the steady state temperature at the interior points? If ∆ ∆ 5 .

20 ) . What (6 mark)

With best wishes Omed Ghareb