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Numerical Methods for Solving Systems of Nonlinear …

Numerical Methods for Solving Systems ofNonlinear EquationsbyCourtney RemaniA project submitted to the Department ofMathematical Sciences in conformity with the requirementsfor Math 4301 (Honour s Seminar)Lakehead UniversityThunder Bay, Ontario, Canadacopyrightc (2012-2013) Courtney RemaniAbstractThis Honours Seminar Project will focus on the Numerical Methods involved in solv-ing Systems of Nonlinear equations . First, we will study Newton s method for solvingmultivariable Nonlinear equations , which involves using the Jacobian matrix. Second, wewill examine a Quasi-Newton which is called Broyden s method; this method has beendescribed as a generalization of the Secant Method. And third, to s solve for nonlin-ear boundary value problems for ordinary differential equations , we will study the FiniteDifference method.

problems only focused on solving nonlinear equations with only one variable, rather than nonlinear equations with several variables. The goal of this paper is to examine three di erent numerical methods that are used to solve systems of nonlinear equations in several variables. The rst method we will look at is Newton’s method.

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