Selected approximation methods for chemical engineering problems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Lyngby
Inst. for Kemiteknik
1970
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Zugl.: Lyngby, Diss. |
| Beschreibung: | 366 S. graph. Darst. |
Internformat
MARC
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| 100 | 1 | |a Villadsen, John |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Selected approximation methods for chemical engineering problems |
| 264 | 1 | |a Lyngby |b Inst. for Kemiteknik |c 1970 | |
| 300 | |a 366 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 500 | |a Zugl.: Lyngby, Diss. | ||
| 650 | 0 | 7 | |a Approximation |0 (DE-588)4002498-2 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
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CONTENTS
Chapter 1 The tools of approximation
1.1 Introduction 1 4
1.2 Basic Definitions 5 35
Operators 5, Functionals and norms 9, Uni¬
form norm 13, Interpolation 17, Example 1 20,
Stretched polynomials 29
1.3 Properties of orthogonal polynomials 36 72
Rodrigues formula 38, Power series 40,
Analytical properties 43, "Value of
(1
Cn = W P2 dx 54, Recurrence formulas 55,
' o
Zeros of P 58, Kernel function 6l, Polynomi¬
als in xz 63, Conclusion 66, Tables of
Jacobi polynomials 70
1.4 Convergence of Ln(f,x) to f(x) 73 103
Weierstrass theorem 78, Convergence in the
weighted mean 80, Convergence in the Lp and
L, norms 83, Uniform convergence 84,
Lebesgue functions 86, Chebyshev polynomials
89, Lebesgue constants for Jacobi polynomi¬
als 94, Jackson's theorems 95, Pejer and
Jackson kernels 99, Analytic and entire
functions 101
1.5 Solution of an interpolatory approximation
problem 104 114
The tubular reactor with axial mixing 104,
Numerical solution 106, Numerical results
108, Discussion 110
1.6 Quadrature formulas 115 157
Definition of Q and Q w 115, The weighted
quadrature Q „ 116, Explicit formulas for
w ^ 119 j Remainder for Gaussian quadrature
120, Lobatto and Radau quadrature 122,
Quadrature formulas of the "derivative
type" 127, Formulas for even functions 144,
Convergence of quadratures based on deriva~
tives 149, Example (Pade approximations
for exp (ax)) 151
1.7 Differential equations 158 207
Indefinite integrals 160, Solution of dif¬
ferential equations 171, Orthogonal collo¬
cation 178, Comparison of orthogonal col¬
location with Runge Kutta methods l8l,
Comparison of orthogonal collocation with
MWR 187, Orthogonal collocation and
quadrature formulas 192
1.8 Solution of a linear boundary value problem
by orthogonal collocation 208 217
Figures to Chapter 1: After page 217.
Chapter 2 Catalyst effectiveness problems
2.1 Introduction 218 220
2.2 The Thiele modulus, Power law kinetics 221 232
Definition of catalyst effectiveness r\
222, Power law kinetics 226
2.3 An analysis of the Weisz Hieks catalyst
effectiveness problem 233 255
Temperature effects 233, A general model
with film resistance included 234, The
Weisz Hicks model 238, Numerical results
for the Weisz Hicks model 240, Asymptotic
results 245, Intraparticle and film
transport restriction 247
2.4 Graphical calculation of effectiveness
factors 256 275
One point collocation 258, Concentration
dependent diffusivity 260, Non isothermal
reactions 267, A criterion for negligible
diffusion effects 271
2.5 Catalyst effectiveness in the oxidation
of S02 to SO 276 296
Equilibrium data 276, Power law kinetics
278, Mars and Maessen's model 280, Mathe¬
matical model 287, Value of D 290, Nume¬
rical results 292, Conclusion 295
Figures to Chapter 2: After page 296.
Chapter 3 Solution of parabolic partial differential
equations
The relevance of the problem 297 298
3.1 Methods for numerical solution of PDE 299 317
Low order difference methods 299, Crank
Nicolson's method 301, Discretization in
the "spatial" coordinate 303, Discretiza¬
tion in the "time" coordinate 311
3.2 Design and optimization of a tubular reac¬
tor for catalytxc oxxdation of o xylene to
phthalic anhydride" 318 341
Mathematical model for the reactor 319,
Discussion of the mathematical model 321,
Optimization problems for a PA reactor 326,
Optimal policies for a real reactor 332,
Conclusion 340
Figures to Chapter 3: After page 34l
Table of symbols 342 351
References 352 360
Summary in danish 361 366
Appendix A Tables of Jacobi Polynomials
Appendix B Orthogonal interpolation
Appendix C Orthogonal collocation
Appendix D Solution of the Weisz Hicks problem |
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| illustrated | Illustrated |
| indexdate | 2025-01-28T09:02:50Z |
| institution | BVB |
| language | English |
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| physical | 366 S. graph. Darst. |
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| publishDate | 1970 |
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| spelling | Villadsen, John Verfasser aut Selected approximation methods for chemical engineering problems Lyngby Inst. for Kemiteknik 1970 366 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Zugl.: Lyngby, Diss. Approximation (DE-588)4002498-2 gnd rswk-swf Chemische Verfahrenstechnik (DE-588)4069941-9 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Approximation (DE-588)4002498-2 s DE-604 Chemische Verfahrenstechnik (DE-588)4069941-9 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005993779&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Villadsen, John Selected approximation methods for chemical engineering problems Approximation (DE-588)4002498-2 gnd Chemische Verfahrenstechnik (DE-588)4069941-9 gnd |
| subject_GND | (DE-588)4002498-2 (DE-588)4069941-9 (DE-588)4113937-9 |
| title | Selected approximation methods for chemical engineering problems |
| title_auth | Selected approximation methods for chemical engineering problems |
| title_exact_search | Selected approximation methods for chemical engineering problems |
| title_full | Selected approximation methods for chemical engineering problems |
| title_fullStr | Selected approximation methods for chemical engineering problems |
| title_full_unstemmed | Selected approximation methods for chemical engineering problems |
| title_short | Selected approximation methods for chemical engineering problems |
| title_sort | selected approximation methods for chemical engineering problems |
| topic | Approximation (DE-588)4002498-2 gnd Chemische Verfahrenstechnik (DE-588)4069941-9 gnd |
| topic_facet | Approximation Chemische Verfahrenstechnik Hochschulschrift |
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