3.10 The equation f(x) = x2 – 5x1/3 + 1 = 0 has a root between x = 2 and x = 2.5. To find the root by using the fixed-point iteration method, the equation has to be written in the form x = g(x). Derive two pos- sible forms for g(x) – one by solving for x from the first term of the equation, and the next by solving for x from the second term of the equation. (a) Determine which form should be used according to the condition in Eq. (3.30). (b) Carry out the first five iterations using both forms of g(x) to confirm your determination in part (a).

3.10 The equation f(x) = x2 – 5x1/3 + 1 = 0 has a root between x = 2 and x = 2.5. To find the root by using the fixed-point iteration method, the equation has to be written in the form x = g(x). Derive two pos- sible forms for g(x) – one by solving for x from the first term of the equation, and the next by solving for x from the second term of the equation. (a) Determine which form should be used according to the condition in Eq. (3.30). (b) Carry out the first five iterations using both forms of g(x) to confirm your determination in part (a).

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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