caa a22 4500 606166270 CHVBK 20210128100657.0 cr unu---uuuuu 210128e20151201xx s 000 0 eng 10.1007/s10440-014-9977-x doi (NATIONALLICENCE)springer-10.1007/s10440-014-9977-x Fazio Riccardo Department of Mathematics and Computer Science, University of Messina, Viale F. Stagno D'Alcontres, 31, 98166, Messina, Italy aut Free Boundary Formulation for BVPs on a Semi-infinite Interval and Non-iterative Transformation Methods [Elektronische Daten] [Riccardo Fazio] This paper is concerned with two examples on the application of the free boundary formulation to BVPs on a semi-infinite interval. In both cases we are able to provide the exact solution of both the BVP and its free boundary formulation. Therefore, these problems can be used as benchmarks for the numerical methods applied to BVPs on a semi-infinite interval and to free BVPs. Moreover, we emphasize how for two classes of free BVPs, we can define non-iterative initial value methods, whereas BVPs are usually solved iteratively. These non-iterative methods can be deduced within Lie's group invariance theory. Then, we show how to apply the non-iterative methods to the two introduced free boundary formulations in order to obtain meaningful numerical results. Finally, we indicate several problems from the literature where our non-iterative transformation methods can be applied. Springer Science+Business Media Dordrecht, 2014 BVPs on a semi-infinite interval nationallicence Free boundary formulation nationallicence Free boundary problems nationallicence Non-iterative numerical method nationallicence Acta Applicandae Mathematicae Springer Netherlands 140/1(2015-12-01), 27-42 0167-8019 140:1<27 2015 140 10440 https://doi.org/10.1007/s10440-014-9977-x text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10440-014-9977-x text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Fazio Riccardo Department of Mathematics and Computer Science, University of Messina, Viale F. Stagno D'Alcontres, 31, 98166, Messina, Italy aut NATIONALLICENCE 773 0- Acta Applicandae Mathematicae Springer Netherlands 140/1(2015-12-01), 27-42 0167-8019 140:1<27 2015 140 10440