Solution File Assignment # 1

Solution File Assignment # 1

MTH603 (Spring 2012)

Total marks: 10

Lecture # 01-08

Due date: 15-04-2012

Dear students as it was told There are 4 questions in the assignment but only one question will be graded. Question 2 will be graded.

Question#1 Marks 10

Find the real root of the equation correct to three decimal places by Bisection method.

Perform three iterations only.

Note: Take any interval in which roots of the equation lie.

Solution:

Consider the interval (0,1).

Since

Since f(0)f(1) < 0 Therefore the root lies between 0 and 1.

1st Iteration

Let say x1 = 0 and x2 = 1

Since

2nd Iteration

Since

3rd Iteration

Therefore 0.875 is the approximate root of the given function after three iteration.

Of course, this is not correct upto three decimal places. For that we need to do more iterations.

Question#2 Marks 10

Use Regula-Fasli method to find the real root of the equation

Correct to four decimal places after three successive approximations in

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

Solution:

Thus root of given equation from 3rd iteration is :

Of course, this is not correct upto four decimal places. For that we need to do more iterations.

Question#3 Marks 10

Apply Newton-Raphson method to determine a root of the equation.

Correct to four decimal places. Only three iterations needed.

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

Solution:

Question#4 Marks 10

Find the root of the equation correct to five decimal places by Secant Method.

Solution:

1st Iteration:

Now

f(x3) = f(0.68507) = cos (0.68507) – 0.68507 = 0.08930

2nd Iteration:

Now

f(x4) = f() =0.00466

3rd Iteration:

Now

f(x5) = f(0.73912) = -0.00006

4th Iteration:

5th Iteration:

Since the value of root in 4th and 5th iteration is same. We stop here and desired root of given equation is