Date of Award
Spring 4-25-2017
Document Type
Honors Project
Degree Name
Bachelor of Science
Department
Mathematics
First Advisor
Lee, Jangwoon
Second Advisor
Helmstutler, Randall
Major or Concentration
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.
Recommended Citation
Dambrose, Rachelle Serena, "Algorithms to Approximate Solutions of Poisson's Equation in Two and Three Dimensions" (2017). Student Research Submissions. 161.
https://scholar.umw.edu/student_research/161