Date of Award

8-1-2014

Degree Name

Master of Science

Department

Mathematics

First Advisor

Schurz, Henri

Abstract

AN ABSTRACT OF THE THESIS OF Matthew Walker, for the Master of Science degree in Mathematics, presented on July 3, 2014, at Southern Illinois University Carbondale. TITLE: THETA METHODS OF NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS AND ERROR ANALYSIS MAJOR PROFESSOR: Dr. H. Schurz This paper will discuss how Theta Methods applied to a Nonlinear Ordinary Differential Equation behave for different critical values of theta. We will look at the stability, consistency, and convergence of the Forward Euler Method, Backward Euler Method, Trapezoidal Method, and the Midpoint Method. All of which can be derived from the Theta Method. After we discuss the convergence we will construct error surfaces and discuss which is the best derived method based on these created surfaces.

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