Project title: A study of modified versions of Newton’s method for solving nonlinear equations
Description of Project: A classical and important problem in scientific computation is solving nonlinear equations. One of the most favourite method for finding the roots of nonlinear equations Is Newton’s method. When applied to locate simple roots, Newton’s method exhibits second-order convergence.
Alms and Objectives: This project aims at studying variants of Newton’s method which provides faster convergence The convergence of the different algorithms will be investigated both analytically and computationally.
Brief Plan of Work: 1. Review of nurnerical solution of nonlinear equations 2. Newton’s rnethod and its variants 3. Convergence analysis 4. Computational experimen.
Prerequisite: Numerical computing.
Bibliography: • McDougall, T. 1., Wotherspoon, S. J. & Barker, P. M. (2019), ‘An accelerated version of Newton’s rnethod with convergence order .sr3 + 1, Results In Applied Mathematics 4, 1-10. • McDougall, T. 1. & Wotherspoon, S. 1. (2014), ‘A simple modification of Newton’s method to achieve convergence of order 1 + a, Applied Mathematics Letters 29, 20-25.

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