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By using Iterative method, find the real roots of equation:, correct to four decimal places.

Evaluate  by using Newton Raphson method, correct to four decimal places.

 

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Please Discuss here about this assignment.Thanks

Our main purpose here discussion not just Solution

We are here with you hands in hands to facilitate your learning and do not appreciate the idea of copying or replicating solutions.

sir yh theek hai

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MTH603 - Numerical Analysis Assignment No. 1 Solution Fall 2016 Due Date: Nov 16, 2016

MTH603 - Numerical Analysis Assignment No. 1 Solution Fall 2016 Due Date: Nov 16, 2016

By using Iterative method, find the real roots of equation:, correct to four decimal places.

Evaluate  by using Newton Raphson method, correct to four decimal places.

 

Iteration Method 
Let the given equation be f(x) = 0 and the value of x to be determined. By using the Iteration method you can find the roots of the equation. To find the root of the equation first we have to write equation like below 
x = pi(x) 
Let x=x0 be an initial approximation of the required root α then the first approximation x1 is given by x1 = pi(x0). 

Similarly for second, thrid and so on. approximation 
x2 = pi(x1
x3 = pi(x2
x4 = pi(x3
xn = pi(xn-1

Iteration Method Example: 
Find the real root of the equation x3 + x 2 = 1 by iteration method. 
Solution: 
We can rewrite the above equation by 
x3 + x 2 - 1 = 0; 
Let f(x) = x3 + x 2 - 1 
f(0) = -1 (positive) 
f(1) = 1 (negative) 
Hence the root value lie between 0 to 1 

x3 + x 2 - 1 = 0 
x2 (x + 1) = 1 
x2 = 1/ (x + 1) 
x = 1/ √(x + 1) 
pi(x) = 1/ √(x + 1) 

Let the initial approximation be x0 = 0.5 

x1 = pi(x0) = 1/√1+ 0.5 = 0.81649 

x2 = pi(x1) = 1/√1+ 0.81649 = 0.74196 

x3 = pi(x2) = 1/√1+ 0.74196 = 0.75767 

x4 = pi(x3) = 1/√1+ 0.75767 = 0.75427 

x5 = pi(x4) = 1/√1+ 0.75427 = 0.75500 

x6 = pi(x5) = 1/√1+ 0.75500 = 0.75485 

x7 = pi(x6) = 1/√1+ 0.75485 = 0.75488 

Since the difference between x6 and x7 are very small, so the root is 0.75488.

Aslamo aelkum 

me is ka sulotion samjna b chahta hon or han kiya he above sulotion 100% ok he ?

plz tell me 

Dear Students Don’t wait for solution post your problems here and discuss ... after discussion a perfect solution will come in a result. So, Start it now, replies here give your comments according to your knowledge and understandings....

Here Is The Solution For this Assignment... Please try to understand the solution rather than replicating it.. Thanks 

After Rewriting the 1st Equation Use 3 and 4 in g(x) to get the initial approximations.

2nd Solution can also be found in Handout..

is this correct solution?

Aslam alikum... can u tell me one thing.... Q1 mein intial value x ki i.e; 

X0 ap ne 3.6 kaise liya hai.... and kya koi b value ly sakty hain yahan for example 0.5 

Wa Alaikum Salam Aese sis...

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2x=7
x=7/2
x=3.5 aai ga x0 =3.5 hojai ga

Sorry bhai smjhi nhi

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