Douglas Rizzolo

Harvey Mudd College Mathematics 2008

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Thesis Proposal: A Method for Approcimating Solutions to Differential Equations via Schauder's Theorem
Thesis: Approximating Solutions to Differential Equations via Fixed Point Theory
Thesis Advisor: Prof. Jon Jacobsen
Second Reader: Prof. Francis E. Su

A Fixed Point Search Algorithm for Approximating Solutions to Differential Equations

Often times a differential equation can be reformulated as a fixed point problem and, when this is done, one of several fixed point theorems can be used to guarantee that a solution exists. Unfortunately, many of these theorems give little insight into how one might find such a solution. Schauder's Theorem is one such theorem. Recently, however, a constructive proof of this theorem was given and this thesis will explore that types of approximations this method produces.