Improved Newton’s Method for Solving Nonlinear Equations

Title: Improved Newton’s Method for Solving Nonlinear Equations

Authors: TGI Fernando

Supervisors: S Weerakoon, GK Watugala, GS Makalanda

Keywords: Convergence, Newton’s method, Improved Newton’s method, Nonlinear equations, Root finding, Order of convergence, Iterative methods

Issue Date: 1998

Publisher: University of Sri Jayewardenepura, Faculty of Graduate Studies, MSc Thesis


An iterative scheme is introduced improving Newton’s method which is widely used for solving nonlinear equations. The method is developed for both functions of one variable and two variables.

Proposed scheme replaces the rectangular approximation of the indefinite integral involved in Newton’s Method by a trapezium. It is shown that the order of convergence of the new method is at least three for functions of one variable.
Computational results overwhelmingly support this theory and the computational order of convergence is even more than three for certain functions.

Algorithms constructed were implemented by using the high level computer language Turbo Pascal (Ver. 7)

Description: This thesis was submitted for the degree of Master of Science and awarded by Faculty of Graduate Studies, University of Sri Jayewardenepura, Sri Lanka.



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