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Secant Method Numericals, Lab Reports of Mathematics

Secant Method Numerical Analysis

Typology: Lab Reports

2023/2024

Uploaded on 12/14/2024

christian-sapitan
christian-sapitan 🇵🇭

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Bulacan State University
College of Engineering
Electrical Engineering Department
EE 303L Numerical Methods and Analysis Laboratory
Student Number: ________________ Date: _____________________
Name: _________________________________________________ CYS: EE – 3____
(Last Name, First Name, MI)
Laboratory Activity 7
Secant Method
Objectives:
1. To find the roots of a single nonlinear equation using Secant Method.
2. To find the roots of equations using MS Excel.
Introduction:
The Newton-Raphson method may be difficult to use when the derivative of the function is challenging
to evaluate. In this case, the secant method may be used wherein the derivative is approximated by a
backward finite divided difference.
xi+1=xif
(
xi
)
(xi1xi)
f
(
xi1
)
f
(
xi
)
The secant method requires two initial estimates of x. Hence, an alternative approach is developed – the
modified secant method, wherein the estimation of the derivative involves a fractional perturbation of
the independent variable to estimate f’(x).
xi+1=xiδ xif
(
xi
)
f
(
xi+δ xi
)
f
(
xi
)
Problem:
Determine the lowest positive root of
f
(
x
)
=7 sin (x)ex1
using
a. Secant method using xi-1 = 0.5 and xi = 0.4, and
b. Modified secant method using xi = 0.3 and
δ=0.01
.
Use the table template below in MS Excel to compute for the approximate root of the equation. Perform
the computation until εa falls below εS = 0.001%. Show up to 6 decimal places.
Sapitan, Christian James M.
2022102855 October 30, 2024
B
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Bulacan State University College of Engineering Electrical Engineering Department EE 303L Numerical Methods and Analysis Laboratory Student Number: ________________ Date: _____________________ Name: _________________________________________________ CYS: EE – 3____ (Last Name, First Name, MI) Laboratory Activity 7 Secant Method Objectives:

  1. To find the roots of a single nonlinear equation using Secant Method.
  2. To find the roots of equations using MS Excel. Introduction: The Newton-Raphson method may be difficult to use when the derivative of the function is challenging to evaluate. In this case, the secant method may be used wherein the derivative is approximated by a backward finite divided difference.

xi + 1 = xi −

f ( xi ) ( xi − 1 − xi )

f ( xi − 1 ) − f ( xi )

The secant method requires two initial estimates of x. Hence, an alternative approach is developed – the modified secant method , wherein the estimation of the derivative involves a fractional perturbation of the independent variable to estimate f’(x).

xi + 1 = xi −

δ xi f ( xi )

f ( xi + δ xi ) − f ( xi )

Problem:

Determine the lowest positive root of f ( x )= 7 sin( x ) e − x^ − 1 using

a. Secant method using xi-1 = 0.5 and xi = 0.4, and

b. Modified secant method using xi = 0.3 and δ =0.01.

Use the table template below in MS Excel to compute for the approximate root of the equation. Perform the computation until εa falls below εS = 0.001%. Show up to 6 decimal places. Sapitan, Christian James M. 2022102855 October 30, 2024 B

Bulacan State University College of Engineering Electrical Engineering Department EE 303L Numerical Methods and Analysis Laboratory Student Number: ________________ Date: _____________________ Name: _________________________________________________ CYS: EE – 3____ (Last Name, First Name, MI) Laboratory Activity 7 Secant Method Screenshot of Excel Output: Screenshot of Excel Worksheet (showing the formula): Sapitan, Christian James M. 2022102855 October 5, 2024 B