Advances in the applications of nonstandard finite difference schemes
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| Sprache: | English |
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Singapore [u.a.]
World Scientific
2005
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| 245 | 1 | 0 | |a Advances in the applications of nonstandard finite difference schemes |c ed. Ronald E. Mickens |
| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 2005 | |
| 300 | |a XIII, 650 S. |b graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1819627779030777856 |
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| adam_text | CONTENTS
Preface v
1 Nonstandard Finite Difference Methods 1
R. E. Mickens
1 Générai Comments .................................... 1
2 L5SFD Methods՝. BasicVrâvcipVes......................... 2
3 Dynamic Consistency..................................... 4
4 Some Outstanding Problems............................... 6
References................................................. 7
2 Application of Nonstandard Finite Difference Schemes
to the Simulation Studies of Robotic Systems 11
R. F. Abo-Shanab, N. Sepehri and C. Q. Wu
1 Introduction............................................ 12
2 Dynamic Model of the Robotic Systems.................... 13
3 Constructing the Discrete Derivatives................... 15
4 Simulation Studies...................................... 18
5 Conclusions ............................................ 44
References................................................. 45
3 Applications of Mickens Finite Differences to Several
Related Boundary Value Problems 47
R. Buckmire
1 Introduction............................................ 47
2 The Buckmire MFD Scheme................................. 48
3 MFD Application to Two Singular Linear Boundary Value
Problems................................................ 53
IX
X
Contents
4 MFD Application to the Cylindrical Bratu-Gel’fand
Problem ................................................ 60
5 MFD Application to the One-Dimensional Bratu Problem . 66
6 Conclusion.............................................. 84
References................................................. 85
4 High Accuracy Nonstandard Finite-Difference Time-
Domain Algorithms for Computational
Electromagnetics: Applications to Optics and
Photonics 89
J. B. Cole
1 Introduction............................................ 89
2 Basic Concepts.......................................... 91
3 High Accuracy FDTD Algorithm for the Absorbing Wave
Equation............................................... 100
4 Nonstandard FDTD Solution of the Conducting Maxwell
Equations ............................................. 103
5 Nonstandard Finite Difference Version of the Mur Absorbing
Boundary............................................... 112
6 Discretization and Numerical Stability ................ 127
7 Numerical Models....................................... 143
8 Light Propagation in Subwavelength Structures.......... 150
9 FDTD Algorithms for Electromagnetic Fields with Surface
Plasmons............................................... 163
10 Summary............................................... 181
References.............................................. 187 5
5 Nonstandard Finite Difference Schemes for Solving
Nonlinear Micro Heat Transport Equations in Double-
Layered Metal Thin Films Exposed to Ultrashort
Pulsed Lasers 191
W. Dai
1 Introduction........................................... 191
2 Governing Equations and an Energy Estimate............. 195
3 Nonstandard Finite Difference Scheme .................. 198
4 Nonlinear Interfacial Problem.......................... 216
5 Conclusion............................................. 225
References................................................. 246
Contents
xi
6 Reliable Finite Difference Schemes with Applications
in Mathematical Ecology 249
D. T. Dimitrov, H. V. Kojouharov and
B. M. Chen-Charpentier
1 Introduction............................................. 250
2 Definitions and Preliminaries............................ 251
3 Numerical Methods for Single-Species Population Models . 253
4 Numerical Methods for Multi-Species Population Models . . 261
5 Numerical Examples....................................... 272
6 Conclusions ............................................. 282
References.................................................. 284
7 Applications of the Non-Standard Finite Difference
Method in Non-Smooth Mechanics 287
Y. Dumont
1 Introduction............................................. 287
2 A Short Introduction to the Theory of Differential
Inclusion................................................ 289
3 Numerical Methods for Differential Inclusions ........... 297
4 Frictional Oscillators....................................303
5 Vibro-Impact Oscillators................................. 311
6 Conclusions ............................................. 334
References.................................................. 337
8 Finite Difference Schemes on Unbounded Domains 343
M. Ehrhardt
1 Introduction............................................. 343
2 Fields of Applications....................................345
3 The Finite Difference Equations.......................... 351
4 Discrete TBCs via Exact Solutions ....................... 358
5 Discrete ABCs through Asymptotic Solutions .............. 362
6 The Continued Fraction Approach.......................... 368
7 The Approximation by the Sum of Exponentials............. 370
8 Numerical Example........................................ 373
9 Future Directions........................................ 378
Appendix A. The Z-Transformation............................ 379
References.................................................. 382
Contents
xii
9 Asymptotically Consistent Non-Standard Finite-
Difference Methods for Solving Mathematical Models
Arising in Population Biology 385
A. B. Gumel, K. C. Patidar and R. J. Spiteri
1 Introduction............................................ 386
2 SIS Model............................................... 387
3 Transmission Dynamics of Two HIV Subtypes............... 396
4 A Predator-Prey Model................................... 402
5 Concluding Remarks and Challenges ...................... 407
References................................................. 420
10 Nonstandard Finite Difference Methods and Biological
Models 423
S. R.-J. Jang
1 Introduction.............................................423
2 Epidemic Models ........................................ 426
3 A Multiple Populations Competition Model................ 448
4 Discussion.............................................. 454
References................................................. 456
11 Robust Discretizations versus Increase of the Time
Step for Chaotic Systems 459
C. Letellier and E. M. A. M. Mendes
1 Introduction............................................ 459
2 Topological Analysis of Chaotic Systems................. 463
3 Motivations for Nonstandard Schemes..................... 469
4 The Nonstandard Mickens Scheme...........................474
5 The Normand and Monaco-Cyrot Scheme..................... 491
6 Conclusion.............................................. 507
References................................................. 509
Contents
xiii
12 Contributions to the Theory of Non-Standard Finite
Difference Methods and Applications to Singular
Perturbation Problems 513
J. M.-S. Lubuma and K. C. Patidar
1 Introduction.............................................. 514
2 Towards a Definition of the Nonstandard Finite
Difference Method......................................... 516
3 Singularly Perturbed First-Order Systems of ODEs...........529
4 Singularly Perturbed Second-Order Problems................ 541
5 Singularly Perturbed Advection-Reaction Problems...........548
6 Singularly Perturbed Reaction-Diffusion Problems...........553
7 Conclusions .............................................. 556
References................................................... 558
13 Frequency Accurate Finite Difference Methods 561
A. L. Perkins, P. A. Orlin and F. Zand
1 Introduction.............................................. 562
2 Average Value Spatial Difference.......................... 562
3 Temporal Derivative....................................... 572
4 Higher Order Spatial Derivatives.......................... 584
5 A Frequency Accurate Finite Difference Scheme for
Burgers Equation.......................................... 597
6 Historical Notes.......................................... 612
References................................................... 614
14 Nonstandard Discretization Methods on Lotka-
Volterra Differential Equations 615
L.-I. W. Roeger
1 Introduction.............................................. 615
2 Two-Dimensional Lotka-Volterra Systems.................... 616
3 The May-Leonard Competitive System........................ 626
4 Three-Dimensional Lotira-Volterra Competitive System . . . 640
5 Conclusions and Open Problems............................. 648
References................................................... 649
|
| any_adam_object | 1 |
| author2 | Mickens, Ronald E. |
| author2_role | edt |
| author2_variant | r e m re rem |
| author_facet | Mickens, Ronald E. |
| building | Verbundindex |
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| dewey-full | 518.64 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 518 - Numerical analysis |
| dewey-raw | 518.64 |
| dewey-search | 518.64 |
| dewey-sort | 3518.64 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-12-23T21:37:31Z |
| institution | BVB |
| isbn | 9812564047 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017441434 |
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| physical | XIII, 650 S. graph. Darst. |
| publishDate | 2005 |
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| publisher | World Scientific |
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| spellingShingle | Advances in the applications of nonstandard finite difference schemes Finite-Differenzen-Methode (DE-588)4194626-1 gnd |
| subject_GND | (DE-588)4194626-1 (DE-588)1071861417 |
| title | Advances in the applications of nonstandard finite difference schemes |
| title_auth | Advances in the applications of nonstandard finite difference schemes |
| title_exact_search | Advances in the applications of nonstandard finite difference schemes |
| title_full | Advances in the applications of nonstandard finite difference schemes ed. Ronald E. Mickens |
| title_fullStr | Advances in the applications of nonstandard finite difference schemes ed. Ronald E. Mickens |
| title_full_unstemmed | Advances in the applications of nonstandard finite difference schemes ed. Ronald E. Mickens |
| title_short | Advances in the applications of nonstandard finite difference schemes |
| title_sort | advances in the applications of nonstandard finite difference schemes |
| topic | Finite-Differenzen-Methode (DE-588)4194626-1 gnd |
| topic_facet | Finite-Differenzen-Methode Konferenzschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017441434&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT mickensronalde advancesintheapplicationsofnonstandardfinitedifferenceschemes |