Free Boundary Formulation for Boundary Value Problems on Semi-Infinite
Intervals: An up to Date Review
Abstract
In this paper, we propose a review of the free boundary formulation for
BVPs defined on semi-infinite intervals. The main idea and theorem are
illustrated, for the reader convenience, by using a class of
second-order BVPs. Moreover, we are able to show the effectiveness of
the proposed approach using two examples where the exact solution both
for the BVPs and their free boundary formulation are available. Then, we
describe the free boundary formulation for a general class of BVPs
governed by an n-order differential equation. In this context, we
report three problems solved using the free boundary formulation. The
reported numerical results, obtained by the iterative transformation
method or Keller’s second-order finite difference method, are found to
be in very good agreement with those available in the literature. The
last result of this research is that, in order to orient the interested
reader, we provide an extensive bibliography. Of course, we may aspect
further and more interesting applications of the free boundary
formulation in the future.