Differential equations, discrete systems and control: economic models
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht [u.a.]
Kluwer Acad. Publ.
1997
|
| Schriftenreihe: | Mathematical modelling
3 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVI, 357 S. |
| ISBN: | 0792346750 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804126230112370688 |
|---|---|
| adam_text | IMAGE 1
DIFFERENTIAL EQUATIONS,
DISCRETE SYSTEMS AND CONTROL ECONOMIC MODELS
BY
ARISTIDE HALANAY
FACULTY OFMATHEMATICS, UNIVERSITY OFBUCHAREST, BUCHAREST, ROMANIA
AND
JUDITA SAMUEL
CENTRE OF MATHEMATICAL STATISTICS, ROMANIAN ACADEMY, BUCHAREST, ROMANIA
KLUWER ACADEMIC PUBLISHERS DORDRECHT / BOSTON / LONDON
IMAGE 2
CONTENTS
PREFACE IX
ABOUT THE NOTATIONS XI
INTRODUCTION XIII
1 LINEAR AND AFFINE DIFFERENTIAL EQUATIONS.
EQUATIONS WITH SEPARATED VARIABLES 1
1.1 DIFFERENTIAL EQUATIONS MODELLING GROWTH PROCESSES 1
1.2 LINEAR DIFFERENTIAL EQUATIONS 5
1.3 LINEAR AFFINE DIFFERENTIAL EQUATIONS 6
1.4 SIMPLEST MODELS OF PRICE EVOLUTION IN A MARKET ECONOMY 3 1.5
DISCRETE - TIME MODELS FOR PRICE EVOLUTION 12
1.6 SIMPLEST MODELS FOR ECONOMIC GROWTH 14
1.7 DISCRETE - TIME MODELS FOR ECONOMIC GROWTH 15
1.8 PRODUCTION FUNCTIONS 16
1.9 EQUATIONS WITH SEPARATED VARIABLES 20
1.10 NOTES AND REFERENCES 22
2 LINEAR DIFFERENTIAL EQUATIONS WITH CONSTANT
COEFFICIENTS 23
2.1 SECOND ORDER DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS 23
2.2 DISCRETE - TIME SECOND ORDER LINEAR EQUATIONS 28
2.3 PRICE EVOLUTION IN THE PRESENCE OF INVENTORIES 31
2.4 ECONOMIC GROWTH MODELS 35
2.5 SECOND ORDER LINEAR AFFINE EQUATIONS 41
2.6 THE PHILLIPS MODEL WITH SEVERAL TYPES OF AUTONOMOUS INVESTMENT 48
2.7 HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS WITH CONSTANT
COEFFICIENTS 57
2.8 DISCRETE - TIME LINEAR AFFINE EQUATIONS 63
2.9 THE SAMUELSON - HICKS MODEL FOR ECONOMIC GROWTH 68
2.10 NOTES AND REFERENCES 73
IMAGE 3
VI
3 L I N E AR S Y S T E MS W I TH C O N S T A NT C O E F F I C I E N TS
74
3.1 GENERAL FORM OF SOLUTIONS 74
3.2 MATRIX EXPONENTIAL 80
3.3 LINEAR AFFINE SYSTEMS 84
3.4 ECONOMIC MODELS 88
3.5 LEONTIEFF - TYPE MODELS 92
3.6 PHASE - PORTRAIT FOR SECOND ORDER LINEAR SYSTEMS WITH CONSTANT
COEFFICIENTS 96
3.7 NOTES AND REFERENCES 102
4 GENERAL THEORY OF NONLINEAR SYSTEMS. STABILITY 103
4.1 EXISTENCE AND UNIQUENESS THEOREM FOR THE INITIAL VALUE PROBLEM 103
4.2 EQUILIBRIA. STABILITY. CONTINUOUS TIME 114
4.3 STABILITY. DISCRETE TIME 120
4.4 DISCRETE-TIME LOGISTIC EQUATION 125
4.5 STAHLE POLYNOMIALS 129
4.6 SOME PROPERTIES OF MATRICES THAT OCCUR IN ECONOMIC MODELS 133
4.7 NOTES AND REFERENCES 143
5 NUMERICAL SOLUTION OF DIFFERENTIAL EQUATIONS 144
5.1 EULER METHOD 144
5.2 RICHARDSON EXTRAPOLATION 147
5.3 PREDICTOR - CORRECTOR METHODS 151
5.4 NUMERICAL QUADRATURE 154
5.5 ADAMS TYPE METHODS 156
5.6 STIFF SYSTEMS 158
5.7 SOME APPLICATIONS OF DIFFERENTIAL EQUATIONS IN NUMERICAL ANALYSIS
AND OPTIMIZATION 160
5.7.1 IMPLICIT FUNCTIONS 160
5.7.2 NONLINEAR EQUATIONS 162
5.7.3 FREE OPTIMIZATION 164
5.7.4 LINEAR PROGRAMMING 167
5.8 NOTES AND REFERENCES 170
6 CONTROL SYSTEMS. STABILIZATION OF LINEAR S Y S T E MS 171
6.1 STABILIZATION PROBLEM. STABILIZATION BY LINEAR STATE FEED-BACK 171
6.2 STABILIZATION OF LINEAR SYSTEMS BY USING A CONTROLLER 180
IMAGE 4
VIT
6.3 STABILIZATION IN AN ECONOMIC GROWTH MODEL 181
6.4 A MONETARY POLICY MODEL 184
6.5 STABILIZATION OF DISCRETE-TIME SYSTEMS 190
6.6 A DISCRETE-TIME MONETARY POLICY MODEL 193
6.7 NOTES AND REFERENCES 197
7 OPTIMAL STABILIZATION 198
7.1 LINEAR-QUADRATIC OPTIMIZATION ON INFINITE HORIZON. CONTINUOUS TIME
198
7.2 APPLICATION TO A PRICE MODEL 209
7.3 OPTIMAL STABILIZATION IN DISCRETE TIME 211
7.4 OPTIMAL STABILIZATION IN A DISCRETE-TIME MODEL OF PRICE EVOLUTION
224
7.5 NOTES AND REFERENCES 227
8 L I N E A R - Q U A D R A T I C O P T I M I Z A T I ON ON FINITE
HORIZON 228
8.1 CONTINUOUS TIME 228
8.2 APPLICATIONS 237
8.3 DISCRETE TIME 247
8.4 APPLICATIONS IN DISCRETE TIME 250
8.5 ATRACKING PROBLEM 254
8.6 A SIMPLE DIFFERENTIAL GAME 263
8.7 NOTES AND REFERENCES 269
9 SOME UNCONSTRAINED D Y N A M IC
OPTIMIZATION PROBLEMS 270
9.1 THE SIMPLEST PROBLEM OF THE CALCULUS OF VARIATIONS 270
9.2 A MACROECONOMIC GROWTH MODEL 278
9.3 A DISCRETE - TIME VARIATIONAL PROBLEM 284
9.4 AN APPLICATION 286
9.5 UNRESTRICTED OPTIMAL CONTROL PROBLEM IN DISCRETE TIME 288 9.6 AN
APPLICATION 291
9.7 OPTIMIZATION WITH LINEAR DYNAMICS AND LINEAR COST. CONTINUOUS TIME
294
9.8 SOME MICROECONOMIC MODELS 297
9.8.1 OPTIMIZATION OF THE MAINTENANCE OF AN EQUIPMENT 297
9.8.2 A FINANCIAL POLICY MODEL AT ENTERPRISE LEVEL 298 9.9 OPTIMIZATION
WITH LINEAR DYNAMICS AND LINEAR COST. DISCRETE TIME 301
I
IMAGE 5
9.10 APPLICATIONS 303
9.11 NOTES AND REFERENCES 305
10 GENERAL PROBLEM OF OPTIMAL CONTROL 306
10.1 PROBLEM STATEMENT. GENERAL THEOREMS 30G
10.1.1 THE OPTIMAL CONTROL PROBLEM 306
10.1.2 NECESSARY OPTIMALITY CONDIT.IONS 309
10.2 OPTIMUM CAPITAL ACCUMULATION UNDER THE MINIMUM TIME OBJECTIVE 315
10.3 REDUCTION OF PROBLEMS WITH FREE INITIAL AND FINAL TIME TO PROBLEMS
ON FIXED HORIZON 320
10.4 AN ABSTRACT MULTIPLIER RULE 327
10.5 PROOFOF THEOREM 10.1 339
10.6 NOTES AND REFERENCES 350
REFERENCES 351
INDEX 355
|
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| author | Halanay, Aristide 1924-1997 Samuel, Judita |
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| dewey-ones | 330 - Economics |
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| dewey-search | 330/.01/183 330/.01/183 21 |
| dewey-sort | 3330 11 3183 |
| dewey-tens | 330 - Economics |
| discipline | Mathematik Wirtschaftswissenschaften |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:14:08Z |
| institution | BVB |
| isbn | 0792346750 |
| language | English |
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| publisher | Kluwer Acad. Publ. |
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| series | Mathematical modelling |
| series2 | Mathematical modelling |
| spelling | Halanay, Aristide 1924-1997 Verfasser (DE-588)113733003 aut Differential equations, discrete systems and control economic models by Aristide Halanay and Judita Samuel Dordrecht [u.a.] Kluwer Acad. Publ. 1997 XVI, 357 S. txt rdacontent n rdamedia nc rdacarrier Mathematical modelling 3 Controleleer gtt Differentiaalvergelijkingen gtt Equações diferenciais larpcal Numerieke wiskunde gtt Differential equations, Linear Discrete-time systems Control theory Optimierung (DE-588)4043664-0 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Optimierung (DE-588)4043664-0 s Differentialgleichung (DE-588)4012249-9 s DE-604 Samuel, Judita Verfasser aut Mathematical modelling 3 (DE-604)BV011613239 3 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007883915&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Halanay, Aristide 1924-1997 Samuel, Judita Differential equations, discrete systems and control economic models Mathematical modelling Controleleer gtt Differentiaalvergelijkingen gtt Equações diferenciais larpcal Numerieke wiskunde gtt Differential equations, Linear Discrete-time systems Control theory Optimierung (DE-588)4043664-0 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| subject_GND | (DE-588)4043664-0 (DE-588)4012249-9 |
| title | Differential equations, discrete systems and control economic models |
| title_auth | Differential equations, discrete systems and control economic models |
| title_exact_search | Differential equations, discrete systems and control economic models |
| title_full | Differential equations, discrete systems and control economic models by Aristide Halanay and Judita Samuel |
| title_fullStr | Differential equations, discrete systems and control economic models by Aristide Halanay and Judita Samuel |
| title_full_unstemmed | Differential equations, discrete systems and control economic models by Aristide Halanay and Judita Samuel |
| title_short | Differential equations, discrete systems and control |
| title_sort | differential equations discrete systems and control economic models |
| title_sub | economic models |
| topic | Controleleer gtt Differentiaalvergelijkingen gtt Equações diferenciais larpcal Numerieke wiskunde gtt Differential equations, Linear Discrete-time systems Control theory Optimierung (DE-588)4043664-0 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| topic_facet | Controleleer Differentiaalvergelijkingen Equações diferenciais Numerieke wiskunde Differential equations, Linear Discrete-time systems Control theory Optimierung Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007883915&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV011613239 |
| work_keys_str_mv | AT halanayaristide differentialequationsdiscretesystemsandcontroleconomicmodels AT samueljudita differentialequationsdiscretesystemsandcontroleconomicmodels |