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

Frontcover
Springer Science & Business Media, 01.01.2003 - 471 Seiten
3 Rezensionen
This book deals with numerical methods for solving partial differential equa tions (PDEs) coupling advection, diffusion and reaction terms, with a focus on time-dependency. A combined treatment is presented of methods for hy perbolic problems, thereby emphasizing the one-way wave equation, meth ods for parabolic problems and methods for stiff and non-stiff ordinary dif ferential equations (ODEs). With regard to time-dependency we have at tempted to present the algorithms and the discussion of their properties for the three different types of differential equations in a unified way by using semi-discretizations, i. e. , the method of lines, whereby the PDE is trans formed into an ODE by a suitable spatial discretization. In addition, for hy perbolic problems we also discuss discretizations that use information based on characteristics. Due to this combination of methods, this book differs substantially from more specialized textbooks that deal exclusively with nu merical methods for either PDEs or ODEs. We treat integration methods suitable for both classes of problems. This combined treatment offers a clear advantage. On the one hand, in the field of numerical ODEs highly valuable methods and results exist which are of practical use for solving time-dependent PDEs, something which is often not fully exploited by numerical PDE researchers. Although many problems can be solved by Euler's method or the Crank-Nicolson method, better alter natives are often available which can significantly reduce the computational effort needed to solve practical problems.
  

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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
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XV
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XVI
48
XVII
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XVIII
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XIX
62
XX
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XXI
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XXIII
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XXIV
77
XXV
81
XXVI
83
XXVII
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XXVIII
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XXIX
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XXX
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XXXI
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XXXII
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XXXIII
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XXXIV
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XXXV
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XXXVI
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XXXVIII
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XXXIX
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XL
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XLI
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XLII
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XLIII
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XLIV
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XLVI
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XLVII
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XLVIII
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XLIX
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L
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LI
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LII
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LIII
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LIV
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LV
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LVI
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LVII
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LVIII
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LIX
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LX
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LXI
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LXIII
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LXIV
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LXV
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LXVI
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LXVIII
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LXIX
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LXX
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LXXI
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LXXIII
209
LXXIV
215
LXXXVI
253
LXXXVII
258
LXXXVIII
261
LXXXIX
263
XC
264
XCI
265
XCII
272
XCIII
278
XCIV
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XCV
283
XCVII
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XCVIII
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XCIX
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C
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CI
295
CII
303
CIII
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CIV
311
CV
316
CVII
321
CVIII
325
CXI
329
CXII
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CXIII
331
CXIV
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CXV
337
CXVI
344
CXVII
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CXIX
351
CXX
359
CXXI
365
CXXII
367
CXXIII
369
CXXV
373
CXXVI
383
CXXVIII
386
CXXIX
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CXXX
393
CXXXI
398
CXXXIII
400
CXXXIV
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CXXXV
405
CXXXVI
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CXXXVIII
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CXXXIX
412
CXL
419
CXLI
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CXLII
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CXLIII
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CXLIV
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CXLVI
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CXLVII
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CXLVIII
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CXLIX
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CL
441
CLI
447
CLII
465
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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.

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