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.

of the numerical methods, as well as the advantages and disadvantages of each method. After a discussion of each of the three methods, we will use the computer program Matlab to solve an example of a nonlinear ordinary di erential equation using both the Finite Di ference method and Newton’s method. 1

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  Using, System, Methods, Solving, Numerical, Matlab, Numerical methods, Nonlinear, Solving systems of nonlinear

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