Principles of Mathematical Modelling

Ideas, Methods, Examples

Alexander A. Samarskii, Alexander P. Mikhailov

348 pages, parution le 19/02/2002

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Résumé

This book demonstrates the versatility of the increasingly multi-disciplinary field of mathematical modelling. The authors consider the principles of model construction and use common approaches to build models from a range of subject areas. Although the contents of the book reflect the interests and experiences of the authors, it includes examples of mathematical modelling in subjects from mechanics to social science. A general approach is adopted where ideas and examples are favoured over rigorous mathematical procedures. This insightful book will be of interest to specialists, teachers and students of this fascinating discipline.

Contents

Introduction

Part I

1. Elementary Mathematical Models
2. Examples of Models Following from the Fundamental Laws of Nature
3. Variational Principles and Mathematical Models
4. Example of the Hierarchy of Models
5. The Universality of Mathematical Models
6. Several Models of Elementary Nonlinear Objects

Part II Derivation of Models from the Fundamental Laws of Nature

1. Conservation of the Mass of Substance
2. Conservation of Energy
3. Conservation of the Number of Particles
4. Joint Application of Several Fundamental Laws

Part III Models Deduced from Variational Principles, Hierarchies of Models

1. Equations of Motion, Variational Principles and Conservation Laws in Mechanics
2. Models of Some Mechanical Systems
3. The Boltzmann Equation and its Derivative Equations

Part IV Models of Some Hardly Formalizable Objects

1. Universality of Mathematical Models
2. Some Models of Financial and Economic Processes
3. Some Rivalry Models
4. Dynamics of Distribution of Power in Hierarchy

Part V

1. Application of Similarity Methods
2. The Maximum Principle and Comparison Theorems
3. An Averaging Method
4. On Transition to Discrete Models

Part VI Mathematical Modeling of Complex Objects

1. Problems of Technology and Ecology
2. Fundamental Problems of Natural Science
3. Computing Experiement With Models of Hardly Formalizable Objects

References
Index

L'auteur - Alexander A. Samarskii

Professor Alexander A. Samarskii is Director of the Institute of Mathematical Modelling at the Russian Academy of Science and has been the leader of the Russian National Program for Mathematical Modelling in Science and Technology since 1985. He is a world-renowned researcher who has obtained outstanding results and contributed grately to the development of these subjects.

L'auteur - Alexander P. Mikhailov

Professor Alexander P Mikhailov is a Head of Department at the Institute of Mathematical Modelling at the Russian Academy of Science and is a Professor of M V Lomonosov Moscow State University. His research interests include mathematical physics, the theory of nonlinear phenomena, mathematical modelling of dissipative structures and mathematical modelling of socio-political processes.

Caractéristiques techniques

	PAPIER
Éditeur(s)	Taylor and Francis Books
Auteur(s)	Alexander A. Samarskii, Alexander P. Mikhailov
Parution	19/02/2002
Nb. de pages	348
Format	17,3 x 24,5
Couverture	Broché
Poids	625g
Intérieur	Noir et Blanc
EAN13	9780415272810
ISBN13	978-0-415-27281-0