Collocation methods for Volterra integral and related functional differential equations:
Collocation based on piecewise polynomial approximation represents a powerful class of methods for the numerical solution of initial-value problems for functional differential and integral equations arising in a wide spectrum of applications, including biological and physical phenomena. The present...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2004
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| Schriftenreihe: | Cambridge monographs on applied and computational mathematics
15 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 Volltext |
| Zusammenfassung: | Collocation based on piecewise polynomial approximation represents a powerful class of methods for the numerical solution of initial-value problems for functional differential and integral equations arising in a wide spectrum of applications, including biological and physical phenomena. The present book introduces the reader to the general principles underlying these methods and then describes in detail their convergence properties when applied to ordinary differential equations, functional equations with (Volterra type) memory terms, delay equations, and differential-algebraic and integral-algebraic equations. Each chapter starts with a self-contained introduction to the relevant theory of the class of equations under consideration. Numerous exercises and examples are supplied, along with extensive historical and bibliographical notes utilising the vast annotated reference list of over 1300 items. In sum, Hermann Brunner has written a treatise that can serve as an introduction for students, a guide for users, and a comprehensive resource for experts |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (xiv, 597 pages) |
| ISBN: | 9780511543234 |
| DOI: | 10.1017/CBO9780511543234 |
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| 246 | 1 | 3 | |a Collocation Methods for Volterra Integral & Related Functional Differential Equations |
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| 500 | |a Title from publisher's bibliographic system (viewed on 05 Oct 2015) | ||
| 505 | 8 | 0 | |g 1 |t The collocation method for ODEs : an introduction |g 2 |t Volterra integral equations with smooth kernels |g 3 |t Volterra integro-differential equations with smooth kernels |g 4 |t Initial-value problems with non-vanishing delays |g 5 |t Initial-value problems with proportional (vanishing) delays |g 6 |t Volterra integral equations with weakly singular kernels |g 7 |t VIDEs with weakly singular kernels |g 8 |t Outlook : integral-algebraic equations and beyond |g 9 |t Epilogue |
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Datensatz im Suchindex
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| author | Brunner, H. 1941- |
| author_facet | Brunner, H. 1941- |
| author_role | aut |
| author_sort | Brunner, H. 1941- |
| author_variant | h b hb |
| building | Verbundindex |
| bvnumber | BV043942126 |
| classification_rvk | SK 640 |
| collection | ZDB-20-CBO |
| contents | The collocation method for ODEs : an introduction Volterra integral equations with smooth kernels Volterra integro-differential equations with smooth kernels Initial-value problems with non-vanishing delays Initial-value problems with proportional (vanishing) delays Volterra integral equations with weakly singular kernels VIDEs with weakly singular kernels Outlook : integral-algebraic equations and beyond Epilogue |
| ctrlnum | (ZDB-20-CBO)CR9780511543234 (OCoLC)967683820 (DE-599)BVBBV043942126 |
| dewey-full | 515/.45 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.45 |
| dewey-search | 515/.45 |
| dewey-sort | 3515 245 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511543234 |
| format | Electronic eBook |
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| id | DE-604.BV043942126 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:17Z |
| institution | BVB |
| isbn | 9780511543234 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029351096 |
| oclc_num | 967683820 |
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| owner | DE-12 DE-92 |
| owner_facet | DE-12 DE-92 |
| physical | 1 online resource (xiv, 597 pages) |
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| publishDate | 2004 |
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| publisher | Cambridge University Press |
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| series2 | Cambridge monographs on applied and computational mathematics |
| spelling | Brunner, H. 1941- Verfasser aut Collocation methods for Volterra integral and related functional differential equations Hermann Brunner Collocation Methods for Volterra Integral & Related Functional Differential Equations Cambridge Cambridge University Press 2004 1 online resource (xiv, 597 pages) txt rdacontent c rdamedia cr rdacarrier Cambridge monographs on applied and computational mathematics 15 Title from publisher's bibliographic system (viewed on 05 Oct 2015) 1 The collocation method for ODEs : an introduction 2 Volterra integral equations with smooth kernels 3 Volterra integro-differential equations with smooth kernels 4 Initial-value problems with non-vanishing delays 5 Initial-value problems with proportional (vanishing) delays 6 Volterra integral equations with weakly singular kernels 7 VIDEs with weakly singular kernels 8 Outlook : integral-algebraic equations and beyond 9 Epilogue Collocation based on piecewise polynomial approximation represents a powerful class of methods for the numerical solution of initial-value problems for functional differential and integral equations arising in a wide spectrum of applications, including biological and physical phenomena. The present book introduces the reader to the general principles underlying these methods and then describes in detail their convergence properties when applied to ordinary differential equations, functional equations with (Volterra type) memory terms, delay equations, and differential-algebraic and integral-algebraic equations. Each chapter starts with a self-contained introduction to the relevant theory of the class of equations under consideration. Numerous exercises and examples are supplied, along with extensive historical and bibliographical notes utilising the vast annotated reference list of over 1300 items. In sum, Hermann Brunner has written a treatise that can serve as an introduction for students, a guide for users, and a comprehensive resource for experts Volterra equations / Numerical solutions Collocation methods Volterra-Gleichungen (DE-588)4137459-9 gnd rswk-swf Kollokationsmethode (DE-588)4164696-4 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Volterra-Gleichungen (DE-588)4137459-9 s Kollokationsmethode (DE-588)4164696-4 s 1\p DE-604 Numerisches Verfahren (DE-588)4128130-5 s 2\p DE-604 Erscheint auch als Druckausgabe 978-0-521-80615-2 https://doi.org/10.1017/CBO9780511543234 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Brunner, H. 1941- Collocation methods for Volterra integral and related functional differential equations The collocation method for ODEs : an introduction Volterra integral equations with smooth kernels Volterra integro-differential equations with smooth kernels Initial-value problems with non-vanishing delays Initial-value problems with proportional (vanishing) delays Volterra integral equations with weakly singular kernels VIDEs with weakly singular kernels Outlook : integral-algebraic equations and beyond Epilogue Volterra equations / Numerical solutions Collocation methods Volterra-Gleichungen (DE-588)4137459-9 gnd Kollokationsmethode (DE-588)4164696-4 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| subject_GND | (DE-588)4137459-9 (DE-588)4164696-4 (DE-588)4128130-5 |
| title | Collocation methods for Volterra integral and related functional differential equations |
| title_alt | Collocation Methods for Volterra Integral & Related Functional Differential Equations The collocation method for ODEs : an introduction Volterra integral equations with smooth kernels Volterra integro-differential equations with smooth kernels Initial-value problems with non-vanishing delays Initial-value problems with proportional (vanishing) delays Volterra integral equations with weakly singular kernels VIDEs with weakly singular kernels Outlook : integral-algebraic equations and beyond Epilogue |
| title_auth | Collocation methods for Volterra integral and related functional differential equations |
| title_exact_search | Collocation methods for Volterra integral and related functional differential equations |
| title_full | Collocation methods for Volterra integral and related functional differential equations Hermann Brunner |
| title_fullStr | Collocation methods for Volterra integral and related functional differential equations Hermann Brunner |
| title_full_unstemmed | Collocation methods for Volterra integral and related functional differential equations Hermann Brunner |
| title_short | Collocation methods for Volterra integral and related functional differential equations |
| title_sort | collocation methods for volterra integral and related functional differential equations |
| topic | Volterra equations / Numerical solutions Collocation methods Volterra-Gleichungen (DE-588)4137459-9 gnd Kollokationsmethode (DE-588)4164696-4 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| topic_facet | Volterra equations / Numerical solutions Collocation methods Volterra-Gleichungen Kollokationsmethode Numerisches Verfahren |
| url | https://doi.org/10.1017/CBO9780511543234 |
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