Numerical Methods and Modelling for Engineering by Richard Khoury & Douglas Wilhelm Harder

Author:Richard Khoury & Douglas Wilhelm Harder
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

Method

Requires

Error

Bisection method

2 bounds

O(h)

False position method

2 bounds

O(h)

Simple fixed-point iteration

1 point

O(h)

Newton’s method

1 point + derivative

O(h 2)

Secant method

2 points

O(h 1.618)

Muller’s method

3 points

O(h 1.839)

8.11 Exercises

1.Approximate the root of the following equations in the respective intervals using the bisection method to a relative error of 0.1.(a) f(x) = x 3 − 3; interval [1, 2]

(b) f(x) = x 2 − 10; interval [3, 4]

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