Date

Spring 4-25-2017

Document Type

Honors Project

First Advisor

Lee, Jangwoon

Second Advisor

Helmstutler, Randall

Degree Name

Bachelor of Science

Major or Concentration

Mathematics

Department

Mathematics

Abstract

The focus of this research was to develop numerical algorithms to approximate solutions to Poisson's equation in two and three dimensions. Numerical analysis of partial differential equations is vital to understanding and modeling these complex problems. A finite difference approximation of Poisson's equation can be used to form a system of linear equations of solutions through a region. A computer program was developed to solve this system with inputs such as boundary conditions and a nonhomogenous source function. Approximate solutions were compared with exact solutions to prove their accuracy. The program was tested with an increasing number of subintervals to ensure that the approximations got closer to the actual solution. Then, an experiment was performed to find the temperatures through a heated piece of aluminum foil to show how this approximation can predict real world phenomenon.

Language

English

Included in

Mathematics Commons

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