Picard's Successive Approximation vs. Banach's Contraction principle
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.
Muhammad N Islam
Primary Advisor's Department
Stander Symposium poster
"Picard's Successive Approximation vs. Banach's Contraction principle" (2019). Stander Symposium Posters. 1545.