A survey of pseudo Runge-Kutta methods
This survey collects the theoretical results in the area of pseudo Runge-Kutta methods (PRK ) for ordinary differential equations and it is a vehicle for a current bibliography from 1966 to 2002. PRK methods require fewer functional evaluations than Runge-Kutta methods of the same order. Byrne and...
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| Format: | Article |
| Language: | English |
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Sapienza Università Editrice
2003-01-01
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| Series: | Rendiconti di Matematica e delle Sue Applicazioni |
| Subjects: | |
| Online Access: | https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/2003(2)/217-234.pdf |
| _version_ | 1811244305981898752 |
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| author | Francesco Aldo Costabile |
| author_facet | Francesco Aldo Costabile |
| author_sort | Francesco Aldo Costabile |
| collection | DOAJ |
| description | This survey collects the theoretical results in the area of pseudo Runge-Kutta methods (PRK ) for ordinary differential equations and it is a vehicle for a current bibliography from 1966 to 2002. PRK methods require fewer functional evaluations than Runge-Kutta methods of the
same order. Byrne and Lambert (1966-1967 ) was the first who considered PRK methods
in significative forms. Afterwards Costabile (1968-1975 ) introduced PRK methods of II and III species as an alternative to the first ones. The latter methods are also autostarting and reduce the cost by 50 percent compared with the similar Runge-Kutta ones. Nakashima (1982-1999 ) improved PRK methods of II species and introduced the implicit methods. Jackiewicz, Tracogna, Bartoszewki, Zennaro, Wanner, Hairer (1991- 2000 ) introduced the modern theory of order, also with variable step-size and embedded and continuous formulas. Finally Bartoszewki and Jackiewicz (2000 ) introduced a PRK code for nonstiff differential systems. PRK methods for special second order differential equations are also studied. |
| first_indexed | 2024-04-12T14:23:36Z |
| format | Article |
| id | doaj.art-de076dbbbb75460397042fb939bd9995 |
| institution | Directory Open Access Journal |
| issn | 1120-7183 2532-3350 |
| language | English |
| last_indexed | 2024-04-12T14:23:36Z |
| publishDate | 2003-01-01 |
| publisher | Sapienza Università Editrice |
| record_format | Article |
| series | Rendiconti di Matematica e delle Sue Applicazioni |
| spelling | doaj.art-de076dbbbb75460397042fb939bd99952022-12-22T03:29:30ZengSapienza Università EditriceRendiconti di Matematica e delle Sue Applicazioni1120-71832532-33502003-01-01232217234A survey of pseudo Runge-Kutta methodsFrancesco Aldo Costabile0Università della CalabriaThis survey collects the theoretical results in the area of pseudo Runge-Kutta methods (PRK ) for ordinary differential equations and it is a vehicle for a current bibliography from 1966 to 2002. PRK methods require fewer functional evaluations than Runge-Kutta methods of the same order. Byrne and Lambert (1966-1967 ) was the first who considered PRK methods in significative forms. Afterwards Costabile (1968-1975 ) introduced PRK methods of II and III species as an alternative to the first ones. The latter methods are also autostarting and reduce the cost by 50 percent compared with the similar Runge-Kutta ones. Nakashima (1982-1999 ) improved PRK methods of II species and introduced the implicit methods. Jackiewicz, Tracogna, Bartoszewki, Zennaro, Wanner, Hairer (1991- 2000 ) introduced the modern theory of order, also with variable step-size and embedded and continuous formulas. Finally Bartoszewki and Jackiewicz (2000 ) introduced a PRK code for nonstiff differential systems. PRK methods for special second order differential equations are also studied.https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/2003(2)/217-234.pdfrunge-kutta methods |
| spellingShingle | Francesco Aldo Costabile A survey of pseudo Runge-Kutta methods Rendiconti di Matematica e delle Sue Applicazioni runge-kutta methods |
| title | A survey of pseudo Runge-Kutta methods |
| title_full | A survey of pseudo Runge-Kutta methods |
| title_fullStr | A survey of pseudo Runge-Kutta methods |
| title_full_unstemmed | A survey of pseudo Runge-Kutta methods |
| title_short | A survey of pseudo Runge-Kutta methods |
| title_sort | survey of pseudo runge kutta methods |
| topic | runge-kutta methods |
| url | https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/2003(2)/217-234.pdf |
| work_keys_str_mv | AT francescoaldocostabile asurveyofpseudorungekuttamethods AT francescoaldocostabile surveyofpseudorungekuttamethods |