Numerical Applications of the Scaling Concept

• Published in: Acta applicandae mathematicae Vol. 55; no. 1; pp. 1 - 25
• Main Author: Fazio, Riccardo
• Format: Journal Article Book Review
• Language: English
• Published: Dordrecht Springer Nature B.V 01.01.1999
• Subjects: Applied mathematics; Bibliographic literature; Dimensional analysis; Eigenvalues; Error analysis; Mathematical analysis; Numerical analysis; Ordinary differential equations; Partial differential equations; Studies
• ISSN: 0167-8019; 1572-9036
• DOI: 10.1023/A:1006197920463

A survey is presented of recent developments in the applications of the scaling concept to numerical analysis. In addition, the paper reports on some relevant topics not covered in existing surveys. Therefore, the present work updates and complements the existing surveys on the subject concerned. Applications of the scaling concept are useful in the numerical treatment of both ordinary and partial differential problems. Applications to boundary-value problems governed by ordinary differential equations are mainly related to their transformation into initial-value problems. Within this context, special emphasis is placed on systems of governing equations, eigenvalue, and free boundary-value problems. An error analysis for a truncated boundary formulation of the Blasius problem is also reported. In writing this paper, the aim was to promote further and more important numerical applications of the scaling concept. Meanwhile, the pertinent bibliography is highlighted and is available on internet as the BIB file sc-gita.bib from the anonymous ftp area at the URL ftp://dipmat.unime.it/pub/papers/fazio/surveys.