Example. Use the fixed-point method with the functiong(x) = 2√₁to solve the equation10- x³x³+4x² 10 = 0in the interval [1,2] for po = 1.5 with a tolerance 10-³.Then use Aitken's A² method to accelerate the fixed point iterations under thesame tolerance.

Fixed point method: To solve f(x)=0 write it in terms of x=g(x) where |g(x)|<1 and then perform…

Answered: Example. Use the fixed-point method…

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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Given the function : f(x) = x³ + 5x² + 7x-20; solve using Secant Method with initial values of (1.000, 2.000) 1st iteration X0 = 1.000 X1 2.000 xnew = 1.241 2nd iteration X0 = 2.000 X1 2.000 xnew 1.296 3rd iteration X0 = 1.241 X1 = 1.296 xnew= 1.310 4th iteration X0 = 1.296 X1 = 1.310 xnew= 1.310 5th iteration X0 = -0.001 X1 = -0.001 xnew= 1.310 f(x0) = -7.000 f(x1) = 22.000 f(xnew) = -1.701 f(x0) = 22.000 f(x1) = -1.701 f(xnew) = -0.353 f(x0) = -1.701 f(x1) = -0.353 f(xnew) -0.001 = f(x0) = -0.001 f(x1) = -0.001 f(xnew) = -0.001 f(x0) = 1.310 f(x1) = -0.001 f(xnew) = -0.001
if f = {(1, −3)} 1) find h(x)=f(−2x−3)+4 2) if k = {(3,5)}, find a and b for which k(x) = af(bx)
Iterate towards an extreme value of the function B(x) using the quadratic interpolation. Use the initial values xo = -2.2- 2-₁, x₁ = 0, X₂ = 8. Calculate three iterations. S = 9 B(x)=ex/2 + -X S+2 9
2) Consider the function f (x) = (x + 4)´ + 1. %3D What is x when f(x) = 0 ? 3) Factor 2x“- + 6x – 3 completely. (Hint: simplify your square root at the end!) Is your solution Real, Rational or Complex?
Q2: Find the root of f(x)=x²-x-2=0 in the range 1
Q2) (a) Determine the roots of f (x) = -6+ 10.5x +9x2- 1.375x graphically. In addition, determine the final root of the function using (b) bisection and (c) false position for (b) and (c) use initial guesses of x = -1 and O and a stopped criterion of 40%.
Determine the root of: f(x) = -13 - 20x + 19x2- 3x with False position method. Use initial guesses of x = -1 and Xu = 1. Perform only 4 iterations, and determine the approximate error at the end of each iteration. %3D A- B I U x2 X2
7

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Example. Use the fixed-point method with the function g(x) =√10-X³ to solve the equation x³+4x² 10 = 0 in the interval [1,2] for po = 1.5 with a tolerance 10-³. Then use Aitken's A² method to accelerate the fixed point iterations under the same tolerance. -