The graduate student's guide to numerical analysis '98: lecture notes from the VIII EPSRC Summer School in Numerical Analysis
Gespeichert in:
| Format: | Tagungsbericht Buch |
|---|---|
| Sprache: | German |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1999
|
| Schriftenreihe: | Springer series in computational mathematics
26 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturangaben |
| Beschreibung: | X, 250 S. graph. Darst. |
| ISBN: | 3540657525 |
Internformat
MARC
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| 245 | 1 | 0 | |a The graduate student's guide to numerical analysis '98 |b lecture notes from the VIII EPSRC Summer School in Numerical Analysis |c Mark Ainsworth ... (ed.) |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1999 | |
| 300 | |a X, 250 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Springer series in computational mathematics |v 26 | |
| 500 | |a Literaturangaben | ||
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| 710 | 2 | |a Engineering and Physical Sciences Research Council |e Sonstige |0 (DE-588)5164381-9 |4 oth | |
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Datensatz im Suchindex
| _version_ | 1804127260977922048 |
|---|---|
| adam_text | Table of Contents
Preface V
A Simple Introduction to Error Estimation for Nonlinear
Hyperbolic Conservation Laws
Bernardo Cockburn 1
1 Introduction 1
2 Some Convection Diffusion Problems 3
2.1 Traffic Flow 4
2.2 Propagation of Phase Transitions 8
2.3 Concluding Remarks 10
3 Continuous Dependence for Nonlinear Convection Diffusion 10
3.1 The Standard Duality Technique and the Adjoint Problem .... 11
3.2 A Technique to Bypass the Resolution of the Adjoint Problem . 12
3.3 A Very Simple Way of Handling the Convective Nonlinearity / 14
3.4 Continuous Dependence Results in i1 like Norms 16
3.5 Allowing the Diffusion Coefficients to Go to Zero 18
3.6 New Continuous Dependence Results 21
3.7 Relaxing the Smoothness in Time of the Approximate Solution
u 24
3.8 The a Posteriori Error Estimate for Non Smooth u 27
3.9 Concluding Remarks 28
4 Continuous Dependence for Nonlinear Convection 29
4.1 Existence and Uniqueness of the Entropy Solution 29
4.2 The Inherited Continuous Dependence Results 30
4.3 Concluding Remarks 32
5 A Posteriori Error Estimates for Continuous Approximations 32
5.1 The Error Estimate 32
5.2 Application to the Engquist Osher Scheme 33
5.3 Explaining the Numerical Results 34
5.4 Another Error Estimate 37
6 A Posteriori Error Estimates for Discontinuous Approximations 39
6.1 The Case of a Finite Number of Smooth Discontinuity Curves . 39
6.2 The Case of a Piecewise Constant Approximation 41
VIII Table of Contents
7 Concluding Remarks 43
7.1 Some Bibliographical Remarks 43
7.2 Open Problems 43
Notes on Accuracy and Stability of Algorithms in Numerical
Linear Algebra
Nicholas J. Higham 47
1 Introduction 47
2 Preliminaries 47
3 Symmetric Indefinite Systems 49
3.1 Block LDLT Factorization 49
3.2 Aasen s Method 54
3.3 Aasen s Method Versus Block LDLT Factorization 59
3.4 Tridiagonal Matrices 59
4 QR Factorization and Constrained Least Squares Problems 60
4.1 Householder QR Factorization 61
4.2 The Constrained Least Squares Problem 67
5 The Singular Value Decomposition and Jacobi s Method 70
5.1 Jacobi s Method 71
5.2 Relative Perturbation Theory 74
5.3 Error Analysis 76
5.4 Other Issues 78
Numerical Analysis of Semilinear Parabolic Problems
Stig Larsson 83
1 The Continuous Problem 83
2 Local a Priori Error Estimates 89
2.1 The Spatially Semidiscrete Problem 90
2.2 A Completely Discrete Scheme 93
3 Shadowing—First Approach 94
3.1 Linearization 95
3.2 Exponential Dichotomies 98
3.3 Shadowing 101
4 A Posteriori Error Estimates 105
4.1 The Error Equation 106
4.2 Local Estimates of the Residual 109
4.3 A Global Error Estimate 112
5 Shadowing—Second Approach 114
Integration Schemes for Molecular Dynamics and Related
Applications
Robert D. Skeel 119
1 Introduction 119
Table of Contents IX
2 Newtonian Dynamics 121
2.1 Properties 121
2.2 The Liouville Equation 123
3 The Leapfrog Method 125
3.1 Derivation 126
3.2 Small At Analysis 128
3.3 Linear Analysis 130
3.4 Small Energy Analysis 132
3.5 Effective Accuracy and Post Processing 134
3.6 Finite Precision Effects 136
4 Other Methods 137
4.1 A Family of Methods 140
4.2 Quest for Accuracy and Stability 141
4.3 The Case for Symplectic Integration 143
5 Multiple Time Steps 145
5.1 The Verlet I/r RESPA/Impulse MTS Method 146
5.2 Partitioning of Interactions 149
5.3 Efficient Implementation 151
5.4 Mollified Impulse MTS Methods 152
6 Constrained Dynamics 153
6.1 Discretization 154
6.2 Solution of the Nonlinear Equations 156
7 Constant Temperature and Constant Pressure Ensembles 156
7.1 Constant Temperature Ensembles 157
7.2 Constant Pressure Ensembles 159
8 Stochastic Dynamics 159
8.1 Langevin Dynamics 160
8.2 Brownian Dynamics 161
A Lie Series and the BCH Formula 162
B Stochastic Processes 164
2.1 Wiener Processes 165
2.2 The Ito Integral 166
2.3 Stochastic Differential Equations 167
2.4 The Fokker Planck Equation 167
2.5 The Ito Formula 168
2.6 Weak Ito Taylor Expansions 169
Numerical Methods for Bifurcation Problems
Alastair Spence and Ivan G. Graham 177
1 Introduction 177
2 Examples 178
3 Newton s Method and the Implicit Function Theorem 183
3.1 Newton s Method for Systems 183
3.2 The Implicit Function Theorem 184
X Table of Contents
3.3 Two Examples 187
4 Computation of Solution Paths 188
4.1 Keller s Pseudo Arclength Continuation [25] 189
4.2 Block Elimination 192
5 The Computation of Fold (Turning) Points 193
5.1 Analysis of Fold Points 194
5.2 Numerical Calculation of Fold Points 196
6 Bifurcation from the Trivial Solution 197
6.1 Scalar Case 197
6.2 n Dimensional Case 199
7 Bifurcation in Nonlinear ODEs 203
7.1 The Shooting Method for ODEs 204
7.2 Analysis of Parameter Dependent ODEs 207
7.3 Calculation of Fold Points in ODEs Using Shooting 208
8 Hopf Bifurcation 209
8.1 Calculation of a Hopf Bifurcation Point 210
8.2 The Detection of Hopf Bifurcations in Large Systems 212
Spectra and Pseudospectra
Lloyd N. Trefethen 217
1 Eigenvalues 217
2 Pseudospectra 225
3 A Matrix Example 233
4 An Operator Example 236
5 History of Pseudospectra 243
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| discipline | Mathematik |
| format | Conference Proceeding Book |
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| spelling | The graduate student's guide to numerical analysis '98 lecture notes from the VIII EPSRC Summer School in Numerical Analysis Mark Ainsworth ... (ed.) Berlin [u.a.] Springer 1999 X, 250 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer series in computational mathematics 26 Literaturangaben Analyse numérique ram Numerical analysis Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 1998 Leicester gnd-content Numerische Mathematik (DE-588)4042805-9 s DE-604 Ainsworth, Mark 1965- Sonstige (DE-588)121031373 oth Engineering and Physical Sciences Research Council Sonstige (DE-588)5164381-9 oth Summer School in Numerical Analysis 8 1998 Leicester Sonstige (DE-588)2176737-3 oth Springer series in computational mathematics 26 (DE-604)BV000012004 26 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008563563&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | The graduate student's guide to numerical analysis '98 lecture notes from the VIII EPSRC Summer School in Numerical Analysis Springer series in computational mathematics Analyse numérique ram Numerical analysis Numerische Mathematik (DE-588)4042805-9 gnd |
| subject_GND | (DE-588)4042805-9 (DE-588)1071861417 |
| title | The graduate student's guide to numerical analysis '98 lecture notes from the VIII EPSRC Summer School in Numerical Analysis |
| title_auth | The graduate student's guide to numerical analysis '98 lecture notes from the VIII EPSRC Summer School in Numerical Analysis |
| title_exact_search | The graduate student's guide to numerical analysis '98 lecture notes from the VIII EPSRC Summer School in Numerical Analysis |
| title_full | The graduate student's guide to numerical analysis '98 lecture notes from the VIII EPSRC Summer School in Numerical Analysis Mark Ainsworth ... (ed.) |
| title_fullStr | The graduate student's guide to numerical analysis '98 lecture notes from the VIII EPSRC Summer School in Numerical Analysis Mark Ainsworth ... (ed.) |
| title_full_unstemmed | The graduate student's guide to numerical analysis '98 lecture notes from the VIII EPSRC Summer School in Numerical Analysis Mark Ainsworth ... (ed.) |
| title_short | The graduate student's guide to numerical analysis '98 |
| title_sort | the graduate student s guide to numerical analysis 98 lecture notes from the viii epsrc summer school in numerical analysis |
| title_sub | lecture notes from the VIII EPSRC Summer School in Numerical Analysis |
| topic | Analyse numérique ram Numerical analysis Numerische Mathematik (DE-588)4042805-9 gnd |
| topic_facet | Analyse numérique Numerical analysis Numerische Mathematik Konferenzschrift 1998 Leicester |
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