Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations

Frontcover
Springer, 01.01.2003 - 471 Seiten
3 Rezensionen

This book describes numerical methods for partial differential equations (PDEs) coupling advection, diffusion and reaction terms, encompassing methods for hyperbolic, parabolic and stiff and nonstiff ordinary differential equations (ODEs). The emphasis lies on time-dependent transport-chemistry problems, describing e.g. the evolution of concentrations in environmental and biological applications. Along with the common topics of stability and convergence, much attention is paid on how to prevent spurious, negative concentrations and oscillations, both in space and time. Many of the theoretical aspects are illustrated by numerical experiments on models from biology, chemistry and physics. A unified approach is followed by emphasizing the method of lines or semi-discretization. In this regard this book differs substantially from more specialized textbooks which deal exclusively with either PDEs or ODEs. This book treats integration methods suitable for both classes of problems and thus is of interest to PDE researchers unfamiliar with advanced numerical ODE methods, as well as to ODE researchers unaware of the vast amount of interesting results on numerical PDEs. The first chapter provides a self-contained introduction to the field and can be used for an undergraduate course on the numerical solution of PDEs. The remaining four chapters are more specialized and of interest to researchers, practitioners and graduate students from numerical mathematics, scientific computing, computational physics and other computational sciences.

  

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Inhalt

I
1
III
3
IV
9
V
14
VI
18
VII
23
IX
27
X
30
LXXVII
222
LXXVIII
226
LXXIX
233
LXXX
239
LXXXII
243
LXXXIII
248
LXXXIV
250
LXXXV
251

XI
35
XII
37
XIII
42
XIV
44
XV
46
XVI
48
XVII
49
XVIII
52
XIX
62
XX
66
XXI
71
XXIII
74
XXIV
77
XXV
81
XXVI
83
XXVII
84
XXVIII
85
XXIX
86
XXX
88
XXXI
92
XXXII
94
XXXIII
99
XXXIV
103
XXXV
111
XXXVI
116
XXXVIII
118
XXXIX
121
XL
124
XLI
127
XLII
128
XLIII
134
XLIV
139
XLVI
140
XLVII
142
XLVIII
144
XLIX
149
L
151
LI
155
LII
158
LIII
161
LIV
166
LV
170
LVI
171
LVII
173
LVIII
174
LIX
181
LX
182
LXI
185
LXIII
189
LXIV
192
LXV
196
LXVI
197
LXVIII
200
LXIX
203
LXX
205
LXXI
206
LXXIII
209
LXXIV
215
LXXXVI
253
LXXXVII
258
LXXXVIII
261
LXXXIX
263
XC
264
XCI
265
XCII
272
XCIII
278
XCIV
281
XCV
283
XCVII
288
XCVIII
291
XCIX
292
C
293
CI
295
CII
303
CIII
308
CIV
311
CV
316
CVII
321
CVIII
325
CXI
329
CXII
330
CXIII
331
CXIV
335
CXV
337
CXVI
344
CXVII
348
CXIX
351
CXX
359
CXXI
365
CXXII
367
CXXIII
369
CXXV
373
CXXVI
383
CXXVIII
386
CXXIX
391
CXXX
393
CXXXI
398
CXXXIII
400
CXXXIV
403
CXXXV
405
CXXXVI
409
CXXXVIII
411
CXXXIX
412
CXL
419
CXLI
420
CXLII
426
CXLIII
430
CXLIV
433
CXLVI
435
CXLVII
436
CXLVIII
438
CXLIX
439
CL
441
CLI
447
CLII
465
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Beliebte Passagen

Seite 464 - ... Protection Agency 600/2-87, 008. United States Department of Energy, (1988), Site-directed Subsurface Environmental Initiative, Five Year Summary and Plan for Fundamental Research in Subsoils and in Groundwater FY1989-1993, April 1988, DOE/ER 03441, Office of Energy Research. Weiser, A., and Wheeler, MF, (1988), On Convergence of Block Centered Finite Differences for Elliptic Problems, SIAM J. Numer. Anal, 25: 351-375. Wheeler, MF, Dawson, CN, Bedient, PB, Chiang, CY, Borden, RC and Rifai, HS,...
Seite 448 - D. [261, 473, 505, 531] (1991) A model for fast computer simulation of waves in excitable media.
Seite 464 - Fully multidimensional flux corrected transport algorithms for fluids, J.
Seite 463 - Convergence and order reduction of diagonally implicit RungeKutta schemes in the method of lines, in Griffiths, Watson: Numerical Analysis, Pitman Research Notes in Mathematics, 220-237, 1986.
Seite 448 - Descombes (2002), Order estimates in time of splitting methods for the nonlinear Schrodinger equation. SIAM J. Numer. Anal. 40, pp.
Seite 463 - Adaptive Methods for Partial Differential Equations. Eds. JE Flaherty, PJ Paslow, MS Shephard, JD Vasilakis, SIAM Proceedings Series, pp.
Seite 464 - Some difference schemes for the solution of the first boundary value problem for linear differential equations with partial derivatives, Thesis (in Russian), Moscow State University.
Seite 447 - An algorithm for ODEs from atmospheric dispersion problems. Appl. Numer. Math. 25, No.
Seite 463 - Explicit Runge-Kutta methods for parabolic partial differential equations. Appl. Numer. Math. 22, pp.

Verweise auf dieses Buch

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Referenzen von Webseiten

The LEM exponential integrator for advection-diffusion-reaction ...
W. Hundsdorfer, jg Verwer, Numerical Solution of Time-Dependent Advection-Diffusion-Reaction equations, Springer Series in Computational Mathematics, vol. ...
portal.acm.org/ citation.cfm?id=1294577

Inexact Newton methods for solving stiff systems of advection ...
Inexact Newton methods for solving stiff systems of advection-diffusion-reaction. equations. Co-authored by:. S. van Veldhuizen ...
www.precond07.enseeiht.fr/ Talks/ veldhuizen/ veldhuizen.pdf

Overview Research Activities 2003 - MAS-1
Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations, Springer Series in Computational Mathematics 33, Springer-Verlag. ...
www.cwi.nl/ publications/ annual-reports/ 2003/ ORA/ HTML/ MAS-1.shtml

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