# MTH603 Numerical Analysis Assignment 1 Solution Spring 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