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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

 

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