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Solve f(x) = x3- 2x - 5 using secant method correct up to 3 decimal places. You may also use excel for the iteration, and handwritten solutions.

Solve f(x) = x3- 2x - 5 using secant method correct up to 3 decimal places. You may also use excel for the iteration, and handwritten solutions.

Advanced Engineering Mathematics
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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Advanced Math - Secant Method

Solve f(x) = x3- 2x - 5 using secant method correct up to 3 decimal places.

You may also use excel for the iteration, and handwritten solutions.

An example is given in the attached picture below:
Example Find the root of f(x) = x7 - 1000 Solution The detailed explanation of the solution is in the video. For the initial iteration, Let's pick x₁ = 2 and x2 = 3 In x3 = 3 x-1000 (-1000)-7 n-1 In-In-1 -1000 37-1000 (37-1000)-27-1000 3-2 Iterations of Secant Method x1 x2 x3 x4 x5 x6 x7 x8 x9 2.423507 2.596515 2.712552 2.679741 2.682598 2.682696 2.682696 We obtain the initial value of x3 as 2.4235065565809. We will continue with the iteration if the value of x is the same given the specified number of precision or after a given number of iteration. After 9 iterations, our value of x is 2.6826957952447.
Transcribed Image Text:Example Find the root of f(x) = x7 - 1000 Solution The detailed explanation of the solution is in the video. For the initial iteration, Let's pick x₁ = 2 and x2 = 3 In x3 = 3 x-1000 (-1000)-7 n-1 In-In-1 -1000 37-1000 (37-1000)-27-1000 3-2 Iterations of Secant Method x1 x2 x3 x4 x5 x6 x7 x8 x9 2.423507 2.596515 2.712552 2.679741 2.682598 2.682696 2.682696 We obtain the initial value of x3 as 2.4235065565809. We will continue with the iteration if the value of x is the same given the specified number of precision or after a given number of iteration. After 9 iterations, our value of x is 2.6826957952447.
Concept Let xo and X₁ are the two initial approximation for the roots of f(x) =0 and f(x₁) respectively are their function values. X2 is the part of intersection of x-axis and the line-joining the points (xo, f(xo)) and (x₁, f(x1)) then x2 is closer than xo and X₁. The equation relating to Xo, X₁ and x2 is found by considering the slope m. f(xn) f(an)-f(n-1) an-n-1 Xn+1 = Xn With the Secant Method, they may not bracket the root and calculates the x2 by the same formula as Regula-Falsi Method but proceeds to the next iteration without bothering about any root bracketing. Let us discuss further in an example.
Transcribed Image Text:Concept Let xo and X₁ are the two initial approximation for the roots of f(x) =0 and f(x₁) respectively are their function values. X2 is the part of intersection of x-axis and the line-joining the points (xo, f(xo)) and (x₁, f(x1)) then x2 is closer than xo and X₁. The equation relating to Xo, X₁ and x2 is found by considering the slope m. f(xn) f(an)-f(n-1) an-n-1 Xn+1 = Xn With the Secant Method, they may not bracket the root and calculates the x2 by the same formula as Regula-Falsi Method but proceeds to the next iteration without bothering about any root bracketing. Let us discuss further in an example.
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