Newton and Secant Methods: Problems and Solutions

Version 1.2.3 (925 KB) by Ismael Abdulrahman
A method to address general problems in Newton's method (and its other version, the secant) including a division by zero and oscillation.
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Updated 20 Mar 2022

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Newton's method is a powerful approach to solving nonlinear equations but it fails (also its approximate, the secant) when the derivative of the function equals zero, approaches zero (diverges or converges very slowly), or due to oscillation between two or more estimates. The attached method provided with six examples programmed in MATLAB shows some methods to avoid such situations.

Cite As

Ismael Abdulrahman (2024). Newton and Secant Methods: Problems and Solutions (https://www.mathworks.com/matlabcentral/fileexchange/107260-newton-and-secant-methods-problems-and-solutions), MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2021b
Compatible with any release
Platform Compatibility
Windows macOS Linux

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2_Recently_Added/4_Matlab_fzero

1_Newton_Problems/1_Division_by_Zero_Polynomial1

1_Newton_Problems/2_Division_by_Zero_Polynomial2

1_Newton_Problems/3_Division_by_Zero_tanh

1_Newton_Problems/4_Division_by_Zero_atan

1_Newton_Problems/5_Division_by_Zero_sin

1_Newton_Problems/6_Division_by_Near_Zero

2_Recently_Added/1_Newton

2_Recently_Added/1_Newton/Newton_OscillationProblem

2_Recently_Added/2_Secant

2_Recently_Added/2_Secant/Standard Secant

2_Recently_Added/3_Halley

Version Published Release Notes
1.2.3

Minor update.
1.2.2

Additional files, examples, and programs.

1.2.1

A total of six examples are provided, each is solved using three methods when the standard Newton's method fails to solve.

1.1.9

Minor changes.

1.1.8

Improvements.
1.1.7

Adding two new examples.
1.1.6

Minor
1.1.5

Minor
1.1.4

Minor
1.1.3

Minor
1.1.2

Minor improvements.

1.1.1

Minor improvements.

1.1.0

Improvements, new methods, and additional examples from a textbook. The case of division by near-zero is added from a textbook.

1.0.7

Minor
1.0.6

Minor
1.0.5

Minor
1.0.4

Minor
1.0.3

Minor
1.0.2

Minor change
1.0.1

Minor change.
1.0.0