Explanation Given: Let f ( x ) = − x 4 + x 2 + A & x 0 = 1 3 Differentiation above equation with respect to x. f ' ( x ) = − 4 x 3 + 2 x To approximate the root of the equation we will use the Newton Raphson method. We know Newton Raphson method. x n + 1 = x n − f ( x n ) f ' ( x n ) ........... (i) Hence we can write x n + 1 = x n − − x n 4 + x n 2 + A − 4 x n 3 + 2 x n ........... (ii) Put n=0 in equation (ii). x 1 = x 0 − − x 0 4 + x 0 2 + A − 4 x 0 3 + 2 x 0 Put x 0 = 1 3 in above equation then

6th Edition

ISBN: 9781465208880

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 3.8, Problem 58PS

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We need to estimate the root of the equation f(x)=−x4+x2+A with the help of Newton Raphson method.

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Chapter 3.8, Problem 57PS

Chapter 3.8, Problem 59PS

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We need to estimate the root of the equation f ( x ) = − x 4 + x 2 + A with the help of Newton Raphson method.

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We need to estimate the root of the equation f(x)=−x4+x2+A with the help of Newton Raphson method.

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Chapter 3 Solutions