Partial difference equations:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London [u.a.]
Taylor & Francis
2003
|
| Series: | Advances in discrete mathematics and applications
3 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 267 S. |
| ISBN: | 0415298849 |
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MARC
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| adam_text | PARTIAL DIFFERENCE EQUATIONS SUI SUN CHENG TSING HUA UNIVERSITY,
REPUBLIC OF CHINA TAYLOR &. FRANCIS TAYLOR & FRANCIS CROUP LONDON AND
NEW YORK CONTENTS SERIES EDITORS PREFACE IX PREFACE XI 1 MODELLING 1
1.1 INTRODUCTION 1 1.2 EXAMPLES 2 1.2.1 DISCRETE HEAT EQUATIONS 2 1.2.2
TWO-LEVEL EQUATIONS 4 1.2.3 MULTI-LEVEL EQUATIONS 10 1.2.4 IMPLICIT
REACTION DIFFUSION EQUATIONS 11 1.2.5 DISCRETE TIME INDEPENDENT
EQUATIONS 12 1.3 AUXILIARY CONDITIONS 14 1.4 NOTES AND REMARKS 16 2
BASIC TOOLS 17 2.1 SUBSETS OF THE LATTICE PLANE 17 2.2 CLASSIFICATIONS
OF PARTIAL DIFFERENCE EQUATIONS 19 2.3 FINITE DIFFERENCES 21 2.4
SUMMABLE INFINITE SEQUENCES 25 2.5 CONVOLUTION OF DOUBLY INFINITE
SEQUENCES 31 2.6 FREQUENCY MEASURES 33 2.7 USEFUL RESULTS FOR MATRICES
40 2.8 DISCRETE GRONWALL INEQUALITIES 43 2.9 MISCELLANEOUS 44 2.10 NOTES
AND REMARKS 45 3 SYMBOLIC CALCULUS 47 3.1 INTRODUCTION 47 3.2
SEMI-INFINITE UNIVARIATE SEQUENCES 47 3.2.1 RING OF SEQUENCES 47 3.2.2
OPERATORS 50 3.2.3 SUMMATION OPERATORS 51 3.2.4 TRANSLATION OR SHIFT
OPERATORS 54 3.2.5 RATIONAL OPERATORS 57 3.2.6 ATTENUATION OPERATORS 59
3.2.7 SEQUENCES AND SERIES OF OPERATORS 60 3.2.8 ALGEBRAIC DERIVATIVES
64 3.2.9 ALGEBRAIC INTEGRALS 69 3.2.10 ORDINARY DIFFERENCE EQUATIONS 71
CONTENTS 3.3 SEMI-INFINITE BIVARIATE SEQUENCES 74 3.3.1 RING OF DOUBLE
SEQUENCES 74 3.3.2 OPERATORS 80 3.3.3 SEPARABLE DOUBLE SEQUENCES 81
3.3.4 BASIC RELATIONS BETWEEN OPERATORS 84 3.3.5 ATTENUATION OPERATORS
85 3.3.6 SEQUENCES AND SERIES OF OPERATORS 86 3.3.7 ALGEBRAIC
DERIVATIVES 90 3.4 NOTES AND REMARKS 92 MONOTONICITY AND CONVEXITY 93
4.1 INTRODUCTION 93 4.2 UNIVARIATE MAXIMUM PRINCIPLES 93 4.3 BIVARIATE
MAXIMUM PRINCIPLES 96 4.4 UNIVARIATE WIRTINGER S INEQUALITIES 100 4.5
BIVARIATE WIRTINGER S INEQUALITIES 103 4.6 NOTES AND REMARKS ILL
EXPLICIT SOLUTIONS 113 5.1 INTRODUCTION 113 5.2 FORMAL METHODS 117 5.3
THE METHOD OF TRANSLATION 120 5.4 THE METHOD OF OPERATORS 121 5.5 THE
METHOD OF SEPARABLE SOLUTIONS 125 5.6 THE METHOD OF CONVOLUTION 128
5.6.1 TWO-LEVEL EQUATIONS OVER THE UPPER HALF LATTICE PLANE . . . 128
5.6.2 THREE-LEVEL EQUATIONS OVER THE UPPER HALF LATTICE PLANE . . 134
5.7 METHOD OF LINEAR SYSTEMS 141 5.8 NOTES AND REMARKS 145 STABILITY 147
6.1 STABILITY CONCEPTS 147 6.2 EQUATIONS OVER CYLINDERS 148 6.2.1 METHOD
OF GENERAL SOLUTIONS 148 6.2.2 METHOD OF MAXIMUM PRINCIPLES 149 6.2.3
METHOD OF ENERGIES 150 6.2.4 METHOD OF FUNCTIONAL INEQUALITIES 151 6.2.5
SPECTRAL METHODS 154 6.2.6 METHOD OF SEPARABLE SOLUTIONS 159 6.3
EQUATIONS OVER HALF PLANES 161 6.3.1 METHOD OF EXACT SOLUTIONS FOR
TWO-LEVEL EQUATIONS 162 6.3.2 METHOD OF EXACT SOLUTIONS FOR THREE-LEVEL
EQUATIONS .... 164 6.3.3 METHOD OF INDUCTION FOR THREE-LEVEL EQUATIONS
169 6.4 EQUATIONS OVER QUADRANTS 173 6.4.1 METHOD OF EXACT SOLUTIONS FOR
A TWO-LEVEL EQUATION 174 6.4.2 METHOD OF INDUCTION FOR A TWO-LEVEL
NONHOMOGENEOUS EQUATION 175 6.4.3 METHOD OF INDUCTION FOR A FOUR-POINT
EQUATION 181 CONTENTS VII 6.4.4 METHOD OF INDUCTION FOR A FOUR-POINT
DELAY EQUATION .... 188 6.4.5 METHOD OF INDUCTION FOR A FIVE-POINT DELAY
EQUATION .... 192 6.5 EQUATIONS OVER FINITE DOMAINS 197 6.6 NOTES AND
REMARKS 200 7 EXISTENCE 201 7.1 INTRODUCTION 201 7.2 TRAVELING WAVES 201
7.3 POSITIVE AND BOUNDED SOLUTIONS 205 7.4 MONOTONE METHOD FOR A FINITE
LAPLACE EQUATION 207 7.5 CONTRACTION METHOD FOR A FINITE LAPLACE
EQUATION 211 7.6 MONOTONE METHOD FOR EVOLUTIONARY EQUATIONS 212 7.7
EIGENVALUE METHOD FOR A BOUNDARY PROBLEM 215 7.8 CONTRACTION METHOD FOR
A BOUNDARY PROBLEM 216 7.9 MONOTONE METHOD FOR BOUNDARY PROBLEMS 217
7.10 NOTES AND REMARKS 222 8 NONEXISTENCE 223 8.1 INTRODUCTION 223 8.2
EQUATIONS OVER THE PLANE 223 8.3 EQUATIONS OVER QUADRANTS 227 8.3.1
THREE-POINT EQUATIONS WITH TWO CONSTANT COEFFICIENTS . . . 227 8.3.2
FOUR-POINT EQUATIONS WITH THREE CONSTANT COEFFICIENTS . . . 228 8.3.3
CHARACTERISTIC INITIAL VALUE PROBLEMS 230 8.3.4 DELAY PARTIAL DIFFERENCE
EQUATIONS 231 8.3.5 FREQUENTLY POSITIVE SOLUTIONS 234 8.4 EQUATIONS OVER
CYLINDERS 235 8.4.1 LINEAR DISCRETE HEAT EQUATION WITH CONSTANT
COEFFICIENTS . . 235 8.4.2 PARABOLIC TYPE EQUATIONS WITH VARIABLE
COEFFICIENTS 238 8.4.3 DISCRETE ELLIPTIC EQUATIONS 241 8.4.4 INITIAL
BOUNDARY VALUE PROBLEMS 244 8.4.5 LINEAR HYBRID FIVE-POINT EQUATIONS 245
8.5 EQUATIONS OVER FINITE DOMAINS 250 8.6 NOTES AND REMARKS 252
BIBLIOGRAPHY 255 INDEX 266
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| discipline | Mathematik |
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| isbn | 0415298849 |
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| physical | XII, 267 S. |
| publishDate | 2003 |
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| publisher | Taylor & Francis |
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| series | Advances in discrete mathematics and applications |
| series2 | Advances in discrete mathematics and applications |
| spelling | Cheng, Sui Sun 1948- Verfasser (DE-588)136106811 aut Partial difference equations Sui Sun Cheng London [u.a.] Taylor & Francis 2003 XII, 267 S. txt rdacontent n rdamedia nc rdacarrier Advances in discrete mathematics and applications 3 Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 s DE-604 Advances in discrete mathematics and applications 3 (DE-604)BV012406028 3 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017478728&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Cheng, Sui Sun 1948- Partial difference equations Advances in discrete mathematics and applications Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| subject_GND | (DE-588)4044779-0 |
| title | Partial difference equations |
| title_auth | Partial difference equations |
| title_exact_search | Partial difference equations |
| title_full | Partial difference equations Sui Sun Cheng |
| title_fullStr | Partial difference equations Sui Sun Cheng |
| title_full_unstemmed | Partial difference equations Sui Sun Cheng |
| title_short | Partial difference equations |
| title_sort | partial difference equations |
| topic | Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| topic_facet | Partielle Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017478728&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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