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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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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....
Aslam alikum... can u tell me one thing.... Q1 mein intial value x ki i.e;
X_{0 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...
2x=7
x=7/2
x=3.5 aai ga x0 =3.5 hojai ga
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