Applications of nonstandard finite difference schemes:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Singapore [u.a.]
World Scientific
2000
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 250 S. graph. Darst. |
| ISBN: | 981024133X |
Internformat
MARC
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| 245 | 1 | 0 | |a Applications of nonstandard finite difference schemes |c ed.: Ronald E. Mickens |
| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 2000 | |
| 300 | |a XII, 250 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Differential equations, Partial |x Numerical solutions | |
| 650 | 4 | |a Finite differences | |
| 655 | 7 | |0 (DE-588)1071861417 |a Konferenzschrift |2 gnd-content | |
| 700 | 1 | |a Mickens, Ronald E. |e Sonstige |4 oth | |
| 856 | 4 | 2 | |m OEBV Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009043962&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
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Datensatz im Suchindex
| _version_ | 1804128031811305472 |
|---|---|
| adam_text | CONT ENT S PREFACE CHAPTER 1 NONSTANDARD FINITE DIFFERENCE SCHEMES
RONALD E . MAEKENS ............................. 1.1 INTRODUCTION
........................... 1.2 EXACT SCHEMES .......................
1.3 NONSTANDARD SCHEMES ............................ 1.4 APPLICATIONS
................. 1.4.1 FIRST-ORDER SCALAR ODE S ................. 1.4.2
A PHOTOCONDUCTION MODEL ................... 1.4.3 THE DUFFING OSCILLATOR
.................. 1.4.4 MIXED PARITY OSCILLATOR 1.4.5 A CUBIC REACTION
PROBLEM IN NEUROPHYSIOLOGY ..... 1.4.6 TIME-INDEPENDENT SCHROEDINGER
EQUATIONS ........ ................. 1.4.7 TRAVELING WAVE SOLUTIONS
........... 1.4.8 LINEAR ADVECTION-DIFFUSION EQUATION
................... 1.4.9 A COMBUSTION MODEL 1.4.10 INFLUENCE OF SPATIAL
DISCRETIZATIONS FOR PDE S ...... .......................... 1.5 FUTURE
DIRECTIONS BIBLIOGRAPHY CHAPTER 2 NONSTANDARD METHODS FOR
ADVECTION-DIFFUSION- REACT ION EQUATIONS HRISTO V . KOJOUHAMV AND BENITO
M . CHEN ............................. 2.1 INTRODUCTION X CONTENTS 2.2
NON-STANDARD METHODS IN ONE DIMENSION ............ 58 2.2.1
ADVECTION-FTEACTION EQUATIONS .............. 59 2.2.1.1 LOGISTIC GROWTH
REACTION TERMS ........ 59 2.2.1.2 LINEAR REACTION TERMS .............
62 2.2.1.3 NONLINEAR REACTION TERMS ........... 64 2.2.2
ADVECTION-DIFFUSION-REACTION EQUATIONS ......... 67 2.3 ERROR ANALYSIS
OF THE NON-STANDARD METHOD ........... 69 2.3.1 ADVECTION-REACTION
EQUATIONS .............. 69 2.3.1.1 ZERO LOCAL TIME- ILUNCATION ERROR
...... 70 2.3.1.2 ZERO LOCAL SPACETRUNCATION ERROR ...... 71 2.3.1.3
INTERPOLATION ERRORS ............... 72 2.3.2
ADVECTION-DIFFUSION-REACTION EQUATIONS ......... 77 2.4 ONE-DIMENSIONAL
NUMERICAL FTESULTS ............... 84 2.4.1 ADVECTION-REACTION EQUATIONS
.............. 85 2.4.2 ADVECTION-DIFFUSION-HRACTION EQUATIONS .........
90 2.5 NON-STANDARD METHODS IN MULTIPLE DIMENSIONS ......... 94 2.5.1
DEVELOPMENT OF THE NON-STANDARD METHOD ....... 94 2.5.2 ERROR ESTIMATES
...................... 98 2.6 SUMMARY .............................. 104
BIBLIOGRAPHY 106 CHAPTER 3 APPLICATION OF NONSTANDARD FINITE DIFFERENCES
TO SOLVE THE WAVE EQUATION AND MAXWELL S EQUATIONS 109 JAMES B . COLE
3.1 INTRODUCTION ............................. 109 3.2 THE
ONE-DIMENSIONAL WAVE EQUATION .............. 111 3.2.1 FITE-DIFFERENTE
TIME-DOMAIN ALGORITHM ........ 111 3.2.2 ALGORITHMIC ERROR
..................... 115 3.2.3 NONSTANDARD FITE DIFIERENCES
.............. 117 3.2.4 ONEDIMENSIONAL SCATTERING ................ 120
3.3 THE TWO- AND THREE-DIMENSIONAL WAVE EQUATION ....... 124 3.3.1
STANDARD FDTD ALGORITHM ................ 124 3.3.2 GENERALIZED
NONSTANDARD FINITE DIFFERENCES - TWO DIMENSIONS
......................... 125 3.2.3 GENERALIZED NONSTANDARD FINITE
DIFFERENCES IN THREE DIMENSIONS ......................... 130 3.4
DISCRETIZATION AND STABILITY .................... 133 CONTENTS XI
........................ 3.4.1 DISCRETIZATION 133
........................... 3.4.2 STABILITY 133 ............. 3.5 NSFD
SOLUTION OF MAXWELL S EQUATIONS 139 3.5.1 THE STANDARD YEE ALGORITHM
............... 139 ................ 3.5.2 NONSTANDARD YEE ALGORITHRN
142 ..... 3.5.3 MAXWELL S EQUATIONS IN A CONDUCTING MEDIUM 146
............... 3.5.4 ELECTROMAGNETIC SIMULATIONS 149
.............................. 3.6 SUMMARY 150
............................. 3.7 CONCLUSION 150 BIBLIOGRAPHY 152
CHAPTER 4 NON-STANDARD DISCRETIZATION METHODS FOR SOME BIOLOGICAL MODELS
155 H . ALKAHBY, F . DANNAN. OND S . ELAYDI
............................. 4.1 INTRODUCTION 155 ........ 4.2
STABILITY OF LOTHVOLTERRA DIFFERENTIAL EQUATIONS 157
...................... 4.3 CLASSICAL DISCRETIZATION 158 ..............
4.4 NONSTANDARD DISCRETIZATION SCHEMES 160 .......... 4.5 COMPETITIVE
AND COOPERATIVE DISCRETE MODELS 161 4.6 PERMANENCE OF DISCRETE
COMPETITIVE AND ........................ COOPERATIVE SYSTEMS 164 4.7
PREDATOR-PREY DISCRETE MODELS .................. 165 4.8 GLOBAL
STABILITY OF COMPETITIVE AND ........................ COOPERATIVE
SYSTEMS 170 4.9 LESLIE PREDATOR-PREY MODEL .................... 172 4.10
OTHER NONSTANDARD NUMERICAL SCHEMES ............. 174 4.11 A KOLMOGOROV
MODEL OF COOPERATIVE SYSTEMS .......... 177 ...........................
4.12 OPEN PROBLEMS 178 BIBLIOGRAPHY 179 CHAPTER 5 AN INTRODUCTION TO
NUMERICAL INTEGRATORS PRE- SERVING PHYSICAL PROPERTIES 181 MARTIN J .
GANDER UND RITA MEYER-SPASCHE ............................. 5.1
INTRODUCTION 182 ..................... 5.2 EXACT DIFFERENTE SCHEMES 184
5.2.1 STANDARD NUMERICAL SCHEMES AS EXACT SCHEMES ..... 184 XII CONTENTS
.............. 5.2.1.1 FIRST ORDER SCHEMES 185 ............. 5.2.1.2
SECOND ORDER SCHEMES 187 ............. 5.2.1.3 HIGHER ORDER SCHEMES 192
............. 5.2.1.4 RUNGE-KUTTA SCHEMES 195 ............. 5.2.2
FUNCTIONAL FITTING RK-METHODS 199 5.2.3 SCHEMES FOR GIVEN DIFFERENTIAL
EQUATIONS ........ 203 5.2.3.1 EXACT SCHEMES FOR GIVEN DIFFERENTIAL
EQUATIONS 203 5.2.3.2 NONSTANDARD SCHEMES FOR PARABOLIC EQUATIONS WITH
BLOW-UP SOLUTIONS: LE-ROUX SCHEMES . . 205 ................. 5.3
DYNAMICS OF DIFFERENCE SCHEMES 208 .............. 5.3.1 CONTINUOUS
DYNAMICAL SYSTEMS 208 ............... 5.3.2 DISCRETE DYNAMICAL SYSTEMS
210 ................... 5.3.3 FORWARD EULER SCHEME 212
.................. 5.3.4 MIDPOINT EULER SCHEME 215 ............. 5.3.5
LIEARLY IMPLICIT EULER SCHEMES 219 ............ 5.3.5.1 DETAILS OF THE
DYNAMICS 221 .................. 5.3.5.2 SUPERSTABILITY 223 ..........
5.3.6 THE LINEARLY HPLICIT LINTRAP SCHEME 224 ............... 5.3.6.1
EXISTENCE INTERVALS 226 ....... 5.3.6.2 ADJOINT AND SELF-ADJOINT SCHEMES
227 ........... 5.3.6.3 CONVERGENCE OF THE SCHEME 228
..................... 5.3.6.4 STABILITY 228 ........... 5.4 SYMPLECTIC
AND ENERGY-CONSERVING SCHEMES 229 5.4.1 CANONICAL HAMILTONIAN SYSTEMS
............. 230 ................ 5.4.1.1 SYMPLECTIC EULER 232 5.4.1.2
THE LINTRAP SCHEME .............. 234 5.4.2 NON-CANONICAL HAMILTONIAN
SYSTEMS ........... 236 5.4.2.1 LINTRAP FOR LOTKA-VOLTERRA ...........
238 5.4.2.2 SYMPLECTIC EULER FOR LOTKA-VOLTERRA ...... 242
......................... 5.5 ACKNOWLEDGEMENT 243 BIBLIOGRAPHY 244
APPENDIX A OTHER RELEVANT REFERENCES LIST OF CONTRIBUTORS
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| genre | (DE-588)1071861417 Konferenzschrift gnd-content |
| genre_facet | Konferenzschrift |
| id | DE-604.BV013266119 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:42:47Z |
| institution | BVB |
| isbn | 981024133X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009043962 |
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| owner_facet | DE-19 DE-BY-UBM DE-83 DE-11 |
| physical | XII, 250 S. graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Applications of nonstandard finite difference schemes ed.: Ronald E. Mickens Singapore [u.a.] World Scientific 2000 XII, 250 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Differential equations, Partial Numerical solutions Finite differences (DE-588)1071861417 Konferenzschrift gnd-content Mickens, Ronald E. Sonstige oth OEBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009043962&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Applications of nonstandard finite difference schemes Differential equations, Partial Numerical solutions Finite differences |
| subject_GND | (DE-588)1071861417 |
| title | Applications of nonstandard finite difference schemes |
| title_auth | Applications of nonstandard finite difference schemes |
| title_exact_search | Applications of nonstandard finite difference schemes |
| title_full | Applications of nonstandard finite difference schemes ed.: Ronald E. Mickens |
| title_fullStr | Applications of nonstandard finite difference schemes ed.: Ronald E. Mickens |
| title_full_unstemmed | Applications of nonstandard finite difference schemes ed.: Ronald E. Mickens |
| title_short | Applications of nonstandard finite difference schemes |
| title_sort | applications of nonstandard finite difference schemes |
| topic | Differential equations, Partial Numerical solutions Finite differences |
| topic_facet | Differential equations, Partial Numerical solutions Finite differences Konferenzschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009043962&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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