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Bisection Method

The document outlines the objectives and methods for solving civil engineering problems using numerical methods, specifically focusing on the bisection method. It describes the bisection method as a technique for finding roots of nonlinear equations by iteratively halving intervals where sign changes occur. Additionally, it includes an example problem and an assignment related to finding roots using the bisection method.

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kiana212003
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99 views8 pages

Bisection Method

The document outlines the objectives and methods for solving civil engineering problems using numerical methods, specifically focusing on the bisection method. It describes the bisection method as a technique for finding roots of nonlinear equations by iteratively halving intervals where sign changes occur. Additionally, it includes an example problem and an assignment related to finding roots using the bisection method.

Uploaded by

kiana212003
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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NUMERICAL

SOLUTIONS TO CE
1
PROBLEMS
ENGR. M.YMOSCOSO
BY: ENGR. MARIA YSABELLA MOSCOSO
1 OBJECTIVES

•Assess the accuracy of the bisection method in finding precise solutions to

civil engineering problems.

•Analyze the convergence rate of the bisection method to determine its

efficiency in different engineering contexts.

•Evaluate the suitability of the bisection method for various types of

numerical problems encountered in civil engineering.


1 NONLINEAR EQUATIONS IN ONE VARIABLE

BRACKETING METHOD

1.1 Bisection Method


1.2 False Position Method
Open Methods

OPEN METHOD

2.1 Fixed-point Method


2.2 Newton – Raphson Method
2.3 3Secant Method

ENGR. M.YMOSCOSO
1 BRACKETING METHOD

If you
4
had a roots problem in the days before computing, you’d
often be told to use “trial and error” to produce the root. That is,
you’d repeatedly make guesses until the function was sufficiently
close to zero. The process was greatly facilitated by the advent
of software tools such as spreadsheets. By allowing you to make
many guesses rapidly, such tools can make the trial-and-error
approach attractive for some problems.

ENGR. M.YMOSCOSO
1 BISECTION METHOD

The bisection method is a variation of the incremental search


method in which the interval is always divided in half. If a
function changes sign over an interval, the function value at
5
the midpoint is evaluated. The location of the root is then
determined as lying within the subinterval where the sign
change occurs. The subinterval then becomes the interval for
the next iteration.

BISECTION METHOD = Binary Chopping


= Interval Halving
= Bolzano’s method

ENGR. M.YMOSCOSO
1 BISECTION METHOD PROCEDURE

Reference: Numerical Methods for Engineers by Chapra and Canale

ENGR. M.YMOSCOSO
1 EXAMPLE 1
Determine the root of 3𝑥 4 + 7𝑥 3 − 15𝑥 2 + 5𝑥 = 17 between [0,2]. Use the bisection method and
perform seven iterations.

ENGR. M.YMOSCOSO
1 ASSIGNMENT

Find the equation where f(x) = 0 with stopping criterion of 0.001. f(x) = 3x+sinx-𝑒 𝑥 .

ENGR. M.YMOSCOSO

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