Numerical Applications of the Scaling Concept
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. Ap...
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| Published in | Acta applicandae mathematicae Vol. 55; no. 1; pp. 1 - 25 |
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| Main Author | |
| Format | Journal Article Book Review |
| Language | English |
| Published |
Dordrecht
Springer Nature B.V
01.01.1999
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0167-8019 1572-9036 |
| DOI | 10.1023/A:1006197920463 |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Fazio, Riccardo |
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| CitedBy_id | crossref_primary_10_1016_S0377_0427_01_00526_X crossref_primary_10_1080_00207160801993224 crossref_primary_10_1016_j_amc_2006_05_002 crossref_primary_10_1016_j_ijnonlinmec_2012_11_011 crossref_primary_10_1016_j_amc_2009_07_019 crossref_primary_10_1007_s10440_008_9244_0 crossref_primary_10_1016_j_jcp_2006_05_024 crossref_primary_10_1080_13873954_2022_2080718 |
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| SubjectTerms | Applied mathematics Bibliographic literature Dimensional analysis Eigenvalues Error analysis Mathematical analysis Numerical analysis Ordinary differential equations Partial differential equations Studies |
| Title | Numerical Applications of the Scaling Concept |
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