Scaling invariance theory and numerical transformation method: A unifying framework

In a transformation method, the numerical solution of a given boundary value problem is obtained by solving one or more related initial value problems. Therefore, a transformation method, like a shooting method, is an initial value method. The peculiar difference between a transformation and a shoot...

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Autor principal: Riccardo Fazio
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Publicado: Elsevier 2020
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spelling oai:doaj.org-article:92b793ce02d24b849d7e80ce31127b772021-12-01T05:05:43ZScaling invariance theory and numerical transformation method: A unifying framework2666-496810.1016/j.apples.2020.100024https://doaj.org/article/92b793ce02d24b849d7e80ce31127b772020-12-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S2666496820300248https://doaj.org/toc/2666-4968In a transformation method, the numerical solution of a given boundary value problem is obtained by solving one or more related initial value problems. Therefore, a transformation method, like a shooting method, is an initial value method. The peculiar difference between a transformation and a shooting method is that the former is conceived and formulated within scaling invariance theory. The main aim of this paper is to propose a unifying framework for numerical transformation methods. The non-iterative method is an extension of the Töpfer’s non-iterative algorithm developed as a simple way to solve the celebrated Blasius problem. As many boundary value problems cannot be solved non-iteratively because they lack the required scaling invariance an iterative extension of the method has been developed. This iterative method provides a simple numerical test for the existence and uniqueness of solutions, as shown by this author in the case of free boundary problems [Appl. Anal., 66 (1997) pp. 89-100] and proved herewith for a wide class of boundary value problems defined on a semi-infinite interval.Riccardo FazioElsevierarticle65L1065L0834B4076D10Engineering (General). Civil engineering (General)TA1-2040ENApplications in Engineering Science, Vol 4, Iss , Pp 100024- (2020)
institution DOAJ
collection DOAJ
language EN
topic 65L10
65L08
34B40
76D10
Engineering (General). Civil engineering (General)
TA1-2040
spellingShingle 65L10
65L08
34B40
76D10
Engineering (General). Civil engineering (General)
TA1-2040
Riccardo Fazio
Scaling invariance theory and numerical transformation method: A unifying framework
description In a transformation method, the numerical solution of a given boundary value problem is obtained by solving one or more related initial value problems. Therefore, a transformation method, like a shooting method, is an initial value method. The peculiar difference between a transformation and a shooting method is that the former is conceived and formulated within scaling invariance theory. The main aim of this paper is to propose a unifying framework for numerical transformation methods. The non-iterative method is an extension of the Töpfer’s non-iterative algorithm developed as a simple way to solve the celebrated Blasius problem. As many boundary value problems cannot be solved non-iteratively because they lack the required scaling invariance an iterative extension of the method has been developed. This iterative method provides a simple numerical test for the existence and uniqueness of solutions, as shown by this author in the case of free boundary problems [Appl. Anal., 66 (1997) pp. 89-100] and proved herewith for a wide class of boundary value problems defined on a semi-infinite interval.
format article
author Riccardo Fazio
author_facet Riccardo Fazio
author_sort Riccardo Fazio
title Scaling invariance theory and numerical transformation method: A unifying framework
title_short Scaling invariance theory and numerical transformation method: A unifying framework
title_full Scaling invariance theory and numerical transformation method: A unifying framework
title_fullStr Scaling invariance theory and numerical transformation method: A unifying framework
title_full_unstemmed Scaling invariance theory and numerical transformation method: A unifying framework
title_sort scaling invariance theory and numerical transformation method: a unifying framework
publisher Elsevier
publishDate 2020
url https://doaj.org/article/92b793ce02d24b849d7e80ce31127b77
work_keys_str_mv AT riccardofazio scalinginvariancetheoryandnumericaltransformationmethodaunifyingframework
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