MTH603 Numerical Analysis Assignment 1 Solution Spring 4th May 2013

Question#1                                                                                            Marks 10

Find the real solution (root) of the equation  by Bisection method.
Perform three iterations only.

Note: Take any interval in which roots of the equation lie.
 Solution:
q#1  with the interval (0,1)

n	x	F(x)
1	0	-5
2	1	-7
3	0.5	-5.375
4	0.75	-5.328
5	0.625	-5.380

Question#2                                                                                             Marks 10

Use Regula-Fasli method to find the real solution (root) of the equation
Correct to four decimal places after three successive approximations in (-2,-1).

Note: All the calculation should be done in the radian mode only.
Solution:

n	x	F(x)
1	-2	-6.0907
2	-1	2.8414
3	-1.3181	-0.3218
4	1.636	8.015
5	1.522	5.523

Question#3                                                                                             Marks 10

Apply Newton-Raphson method to determine solution (root) of the equation.
Correct to three decimal places using the initial approximation.
Only three iterations needed.

Note: All the calculation should be done in the radian mode only.

Question#4                                                                                             Marks 10

Find the solution (root) correct to 4 decimal places of the equation  using Secant Method.

Note: Take any interval in which roots of the equation lie and all the calculation should
be done in the radian mode only.
Solution:

n	x	F(x)
1	1	11
2	5	27.83
3	-1.6139	2.1739
4	1.32707	4.174214
5	-4.8096	22.1614