Partial Differential Equations: New Methods for Their Treatment and Solution
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
1985
|
| Schriftenreihe: | Mathematics and Its Applications
15 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The purpose of this book is to present some new methods in the treatment of partial differential equations. Some of these methods lead to effective numerical algorithms when combined with the digital computer. Also presented is a useful chapter on Green's functions which generalizes, after an introduction, to new methods of obtaining Green's functions for partial differential operators. Finally some very new material is presented on solving partial differential equations by Adomian's decomposition methodology. This method can yield realistic computable solutions for linear or non linear cases even for strong nonlinearities, and also for deterministic or stochastic cases - again even if strong stochasticity is involved. Some interesting examples are discussed here and are to be followed by a book dealing with frontier applications in physics and engineering. In Chapter I, it is shown that a use of positive operators can lead to monotone convergence for various classes of nonlinear partial differential equations. In Chapter II, the utility of conservation technique is shown. These techniques are suggested by physical principles. In Chapter III, it is shown that dyn~mic programming applied to variational problems leads to interesting classes of nonlinear partial differential equations. In Chapter IV, this is investigated in greater detail. In Chapter V, we show. that the use of a transformation suggested by dynamic programming leads to a new method of successive approximations |
| Beschreibung: | 1 Online-Ressource (XVII, 290 p) |
| ISBN: | 9789400952096 9789401088046 |
| DOI: | 10.1007/978-94-009-5209-6 |
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| discipline | Mathematik |
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| id | DE-604.BV042423733 |
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| indexdate | 2024-07-10T01:21:14Z |
| institution | BVB |
| isbn | 9789400952096 9789401088046 |
| language | English |
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| spelling | Bellman, Richard Verfasser aut Partial Differential Equations New Methods for Their Treatment and Solution by Richard Bellman, George Adomian Dordrecht Springer Netherlands 1985 1 Online-Ressource (XVII, 290 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 15 The purpose of this book is to present some new methods in the treatment of partial differential equations. Some of these methods lead to effective numerical algorithms when combined with the digital computer. Also presented is a useful chapter on Green's functions which generalizes, after an introduction, to new methods of obtaining Green's functions for partial differential operators. Finally some very new material is presented on solving partial differential equations by Adomian's decomposition methodology. This method can yield realistic computable solutions for linear or non linear cases even for strong nonlinearities, and also for deterministic or stochastic cases - again even if strong stochasticity is involved. Some interesting examples are discussed here and are to be followed by a book dealing with frontier applications in physics and engineering. In Chapter I, it is shown that a use of positive operators can lead to monotone convergence for various classes of nonlinear partial differential equations. In Chapter II, the utility of conservation technique is shown. These techniques are suggested by physical principles. In Chapter III, it is shown that dyn~mic programming applied to variational problems leads to interesting classes of nonlinear partial differential equations. In Chapter IV, this is investigated in greater detail. In Chapter V, we show. that the use of a transformation suggested by dynamic programming leads to a new method of successive approximations Mathematics Global analysis (Mathematics) Analysis Mathematik Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 s 1\p DE-604 Adomian, George Sonstige oth https://doi.org/10.1007/978-94-009-5209-6 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bellman, Richard Partial Differential Equations New Methods for Their Treatment and Solution Mathematics Global analysis (Mathematics) Analysis Mathematik Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| subject_GND | (DE-588)4044779-0 |
| title | Partial Differential Equations New Methods for Their Treatment and Solution |
| title_auth | Partial Differential Equations New Methods for Their Treatment and Solution |
| title_exact_search | Partial Differential Equations New Methods for Their Treatment and Solution |
| title_full | Partial Differential Equations New Methods for Their Treatment and Solution by Richard Bellman, George Adomian |
| title_fullStr | Partial Differential Equations New Methods for Their Treatment and Solution by Richard Bellman, George Adomian |
| title_full_unstemmed | Partial Differential Equations New Methods for Their Treatment and Solution by Richard Bellman, George Adomian |
| title_short | Partial Differential Equations |
| title_sort | partial differential equations new methods for their treatment and solution |
| title_sub | New Methods for Their Treatment and Solution |
| topic | Mathematics Global analysis (Mathematics) Analysis Mathematik Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Analysis Mathematik Partielle Differentialgleichung |
| url | https://doi.org/10.1007/978-94-009-5209-6 |
| work_keys_str_mv | AT bellmanrichard partialdifferentialequationsnewmethodsfortheirtreatmentandsolution AT adomiangeorge partialdifferentialequationsnewmethodsfortheirtreatmentandsolution |