Picard's Successive Approximation vs. Banach's Contraction principle

Authors

Presenter(s)

Leah Marie Squiller

Files

Description

The existence of a unique solution to the initial value problem: x’(t)=f(t,x) x(t0,)=x0 , can be obtained employing Banach’s contraction principle or Picard’s successive approximation method. Generally, the norm that is used in the contraction principle is the supremum norm that requires a condition that is not needed in the successive approximation method. Therefore, it seems as if the successive approximation method is a superior method. The objective of this project is to show that these two methods are equally efficient. This is due to the fact that the condition that was needed in the contraction principle can be eliminated by using a different norm that is equivalent to the supremum norm.

Publication Date

4-24-2019

Project Designation

Capstone Project

Primary Advisor

Muhammad N. Islam

Primary Advisor's Department

Mathematics

Keywords

Stander Symposium project

Recommended Citation

"Picard's Successive Approximation vs. Banach's Contraction principle" (2019). Stander Symposium Projects. 1545.
https://ecommons.udayton.edu/stander_posters/1545