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
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2020
Materias:	65L10 65L08 34B40 76D10 Engineering (General). Civil engineering (General) TA1-2040
Acceso en línea:	https://doaj.org/article/92b793ce02d24b849d7e80ce31127b77
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id	oai:doaj.org-article:92b793ce02d24b849d7e80ce31127b77
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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
_version_	1718405555756728320

Scaling invariance theory and numerical transformation method: A unifying framework

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