Order stars:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London [u.a.]
Chapman & Hall
1991
|
| Ausgabe: | 1. ed. |
| Schriftenreihe: | Applied mathematics and mathematical computation
2 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 248 S. graph. Darst. |
| ISBN: | 0412352605 |
Internformat
MARC
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| 100 | 1 | |a Iserles, Arieh |d 1947- |e Verfasser |0 (DE-588)172163641 |4 aut | |
| 245 | 1 | 0 | |a Order stars |c A. Iserles and S. P. Nørsett |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a London [u.a.] |b Chapman & Hall |c 1991 | |
| 300 | |a XI, 248 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Applied mathematics and mathematical computation |v 2 | |
| 650 | 4 | |a Approximation theory | |
| 650 | 4 | |a Differential equations |x Numerical solutions | |
| 650 | 4 | |a Order stars (Mathematics) | |
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Datensatz im Suchindex
| _version_ | 1809404445936582656 |
|---|---|
| adam_text |
Contents
Preface viii
1 Introduction 1
2 General order stars 9
2.1 Order stars of the first kind 9
2.2 Essential singularities 16
2.3 Order stars of the second kind 22
3 Rational approximants to the exponential 28
3.1 Introduction 28
3.2 Collocation 29
3.3 Obrechkoff methods 32
3.4 Examples of approximants 35
3.5 Order barriers 41
3.6 Degree of real interpolation 42
3.7 Symmetric approximants with real poles 45
4 A acceptability barriers 50
4.1 Motivation 50
4.2 Maximal approximants 51
4.3 Hairer's representation of rational approximants 57
4.4 Restricted approximants 63
4.5 Interpolation with p restricted approximants 71
4.6 Complex fitting 76
5 Multistep methods 92
5.1 The first Dahlquist barrier 92
5.2 Order stars on Riemann surfaces 103
vi CONTENTS
5.3 The Daniel Moore conjecture and its solution 112
5.4 The Jeltsch Nevanlinna comparison theorem 116
6 The advection equation 120
6.1 Order and stability conditions 120
6.2 The influence of boundaries on stability 129
6.3 A barrier for semi discretizations 133
6.4 Stable full discretizations 141
6.5 A barrier for full discretizations 148
7 The diffusion equation 155
7.1 Methods of optimal order 155
7.2 Pade approximants to /((log z)2) 161
7.3 The order of optimal methods 163
7.4 Stability of optimal methods 171
8 Pade approximants 177
8.1 Block numbers of Pade tableaux 177
8.2 Nonvanishing functions 181
8.3 Functions with an infinite number of zeros 185
9 Contractive approximation 193
9.1 Zeros and contractions 193
9.2 The Pick Nevanlinna interpolation problem 202
10 Open problems 207
Problem 1 /4(a) acceptability of Pade
approximants to exp z 208
Problem 2 Restricted Pade approximants to exp z 209
Problem 3 Polynomial aproximants to exp z 211
Problem 4 Multipoint Pade approximants to exp z 212
Problem 5 Multipoint restricted Pade
approximants to exp z 214
Problem 6 The root condition for BDF 215
Problem 7 The root condition for general
algebraic functions 217
Problem 8 Jeltsch Nevanlinna comparison theorems 218
Problem 9 Order reduction for Runge Kutta methods 218
Problem 10 Multistep methods for the advection
equation 221
CONTENTS vii
Problem 11 Advection equation with two space
variables 224
Problem 12 Pade approximants to slit functions 225
Problem 13 Complex approximation and
interpolation 226
Bibliography 228
Name index 239
Subject index 242 |
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| id | DE-604.BV004737530 |
| illustrated | Illustrated |
| indexdate | 2024-09-06T00:29:07Z |
| institution | BVB |
| isbn | 0412352605 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002915235 |
| oclc_num | 25966780 |
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| owner_facet | DE-384 DE-91G DE-BY-TUM DE-20 DE-19 DE-BY-UBM DE-11 DE-29T |
| physical | XI, 248 S. graph. Darst. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | Chapman & Hall |
| record_format | marc |
| series | Applied mathematics and mathematical computation |
| series2 | Applied mathematics and mathematical computation |
| spelling | Iserles, Arieh 1947- Verfasser (DE-588)172163641 aut Order stars A. Iserles and S. P. Nørsett 1. ed. London [u.a.] Chapman & Hall 1991 XI, 248 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Applied mathematics and mathematical computation 2 Approximation theory Differential equations Numerical solutions Order stars (Mathematics) Padé-Näherungsbruch (DE-588)4173061-6 gnd rswk-swf Padé-Näherungsbruch (DE-588)4173061-6 s DE-604 Nørsett, Syvert P. 1944-2024 Verfasser (DE-588)13758718X aut Applied mathematics and mathematical computation 2 (DE-604)BV006188231 2 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002915235&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Iserles, Arieh 1947- Nørsett, Syvert P. 1944-2024 Order stars Applied mathematics and mathematical computation Approximation theory Differential equations Numerical solutions Order stars (Mathematics) Padé-Näherungsbruch (DE-588)4173061-6 gnd |
| subject_GND | (DE-588)4173061-6 |
| title | Order stars |
| title_auth | Order stars |
| title_exact_search | Order stars |
| title_full | Order stars A. Iserles and S. P. Nørsett |
| title_fullStr | Order stars A. Iserles and S. P. Nørsett |
| title_full_unstemmed | Order stars A. Iserles and S. P. Nørsett |
| title_short | Order stars |
| title_sort | order stars |
| topic | Approximation theory Differential equations Numerical solutions Order stars (Mathematics) Padé-Näherungsbruch (DE-588)4173061-6 gnd |
| topic_facet | Approximation theory Differential equations Numerical solutions Order stars (Mathematics) Padé-Näherungsbruch |
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