The Numerical Treatment of Differential Equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1960
|
| Ausgabe: | 2nd Printing of the 3rd Edition |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | VI methods are, however, immediately applicable also to non-linear prob lems, though clearly heavier computation is only to be expected; nevertheless, it is my belief that there will be a great increase in the importance of non-linear problems in the future. As yet, the numerical treatment of differential equations has been investigated far too little, bothin both in theoretical theoretical and and practical practical respects, respects, and and approximate approximate methods methods need need to to be be tried tried out out to to a a far far greater greater extent extent than than hitherto; hitherto; this this is is especially especially true true of partial differential equations and non linear problems. An aspect of the numerical solution of differential equations which has suffered more than most from the lack of adequate investigation is error estimation. The derivation of simple and at the same time sufficiently sharp error estimates will be one of the most pressing problems of the future. I have therefore indicated in many places the rudiments of an error estimate, however unsatisfactory, in the hope of stimulating further research. Indeed, in this respect the book can only be regarded as an introduction. Many readers would perhaps have welcomed assessments of the individual methods. At some points where well-tried methods are dealt with I have made critical comparisons between them; but in general I have avoided passing judgement, for this requires greater experience of computing than is at my disposal |
| Beschreibung: | 1 Online-Ressource (XV, 568 p) |
| ISBN: | 9783662055007 9783662054567 |
| DOI: | 10.1007/978-3-662-05500-7 |
Internformat
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| 500 | |a VI methods are, however, immediately applicable also to non-linear prob lems, though clearly heavier computation is only to be expected; nevertheless, it is my belief that there will be a great increase in the importance of non-linear problems in the future. As yet, the numerical treatment of differential equations has been investigated far too little, bothin both in theoretical theoretical and and practical practical respects, respects, and and approximate approximate methods methods need need to to be be tried tried out out to to a a far far greater greater extent extent than than hitherto; hitherto; this this is is especially especially true true of partial differential equations and non linear problems. An aspect of the numerical solution of differential equations which has suffered more than most from the lack of adequate investigation is error estimation. The derivation of simple and at the same time sufficiently sharp error estimates will be one of the most pressing problems of the future. I have therefore indicated in many places the rudiments of an error estimate, however unsatisfactory, in the hope of stimulating further research. Indeed, in this respect the book can only be regarded as an introduction. Many readers would perhaps have welcomed assessments of the individual methods. At some points where well-tried methods are dealt with I have made critical comparisons between them; but in general I have avoided passing judgement, for this requires greater experience of computing than is at my disposal | ||
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Datensatz im Suchindex
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|---|---|
| any_adam_object | |
| author | Collatz, Lothar 1910-1990 |
| author_GND | (DE-588)118521543 |
| author_facet | Collatz, Lothar 1910-1990 |
| author_role | aut |
| author_sort | Collatz, Lothar 1910-1990 |
| author_variant | l c lc |
| building | Verbundindex |
| bvnumber | BV042423356 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)864105173 (DE-599)BVBBV042423356 |
| dewey-full | 518 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 518 - Numerical analysis |
| dewey-raw | 518 |
| dewey-search | 518 |
| dewey-sort | 3518 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-662-05500-7 |
| edition | 2nd Printing of the 3rd Edition |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:13Z |
| institution | BVB |
| isbn | 9783662055007 9783662054567 |
| language | English |
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| spelling | Collatz, Lothar 1910-1990 Verfasser (DE-588)118521543 aut The Numerical Treatment of Differential Equations by Lothar Collatz 2nd Printing of the 3rd Edition Berlin, Heidelberg Springer Berlin Heidelberg 1960 1 Online-Ressource (XV, 568 p) txt rdacontent c rdamedia cr rdacarrier VI methods are, however, immediately applicable also to non-linear prob lems, though clearly heavier computation is only to be expected; nevertheless, it is my belief that there will be a great increase in the importance of non-linear problems in the future. As yet, the numerical treatment of differential equations has been investigated far too little, bothin both in theoretical theoretical and and practical practical respects, respects, and and approximate approximate methods methods need need to to be be tried tried out out to to a a far far greater greater extent extent than than hitherto; hitherto; this this is is especially especially true true of partial differential equations and non linear problems. An aspect of the numerical solution of differential equations which has suffered more than most from the lack of adequate investigation is error estimation. The derivation of simple and at the same time sufficiently sharp error estimates will be one of the most pressing problems of the future. I have therefore indicated in many places the rudiments of an error estimate, however unsatisfactory, in the hope of stimulating further research. Indeed, in this respect the book can only be regarded as an introduction. Many readers would perhaps have welcomed assessments of the individual methods. At some points where well-tried methods are dealt with I have made critical comparisons between them; but in general I have avoided passing judgement, for this requires greater experience of computing than is at my disposal Mathematics Computer science / Mathematics Numerical analysis Numerical Analysis Computational Mathematics and Numerical Analysis Informatik Mathematik Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 s Numerisches Verfahren (DE-588)4128130-5 s 1\p DE-604 Numerische Mathematik (DE-588)4042805-9 s 2\p DE-604 https://doi.org/10.1007/978-3-662-05500-7 Verlag 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 | Collatz, Lothar 1910-1990 The Numerical Treatment of Differential Equations Mathematics Computer science / Mathematics Numerical analysis Numerical Analysis Computational Mathematics and Numerical Analysis Informatik Mathematik Numerische Mathematik (DE-588)4042805-9 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| subject_GND | (DE-588)4042805-9 (DE-588)4128130-5 (DE-588)4012249-9 |
| title | The Numerical Treatment of Differential Equations |
| title_auth | The Numerical Treatment of Differential Equations |
| title_exact_search | The Numerical Treatment of Differential Equations |
| title_full | The Numerical Treatment of Differential Equations by Lothar Collatz |
| title_fullStr | The Numerical Treatment of Differential Equations by Lothar Collatz |
| title_full_unstemmed | The Numerical Treatment of Differential Equations by Lothar Collatz |
| title_short | The Numerical Treatment of Differential Equations |
| title_sort | the numerical treatment of differential equations |
| topic | Mathematics Computer science / Mathematics Numerical analysis Numerical Analysis Computational Mathematics and Numerical Analysis Informatik Mathematik Numerische Mathematik (DE-588)4042805-9 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| topic_facet | Mathematics Computer science / Mathematics Numerical analysis Numerical Analysis Computational Mathematics and Numerical Analysis Informatik Mathematik Numerische Mathematik Numerisches Verfahren Differentialgleichung |
| url | https://doi.org/10.1007/978-3-662-05500-7 |
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