Mathematical Modeling And Simulation

Kai Velten

Mathematical Modeling and Simulation
Introduction for Scientists and Engineers

Kai Velten Mathematical Modeling and Simulation

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Kai Velten

MathematicalModeling and Simulation
Introduction for Scientists and Engineers

The Author Prof. Dr. Kai Velten RheinMain University of Applied Sciences Geisenheim, Germany Kai.Velten@gmail.com Cover Simulated soil moisture isosurfaces in an asparagus ridge (details are explained in the text). Computer simulation performed by the author.

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V

Contents
Preface 1 1.1 1.2 1.2.1 1.2.2 1.2.3 1.2.4 1.2.5 1.3 1.3.1 1.3.2 1.3.3 1.4 1.5 1.5.1 1.5.2 1.5.3 1.5.4 1.5.4.1 1.5.4.2 1.5.5 1.5.6 1.6 1.6.1 1.6.2 1.6.3 1.7 1.7.1 1.7.2 1.7.3 XIII

Principles of Mathematical Modeling 1 AComplex World Needs Models 1 Systems, Models, Simulations 3 Teleological Nature of Modeling and Simulation 4 Modeling and Simulation Scheme 4 Simulation 7 System 7 Conceptual and Physical Models 8 Mathematics as a Natural Modeling Language 9 Input–Output Systems 9 General Form of Experimental Data 10 Distinguished Role of Numerical Data 10 Definition of Mathematical Models 11 Examples and SomeMore Definitions 13 State Variables and System Parameters 15 Using Computer Algebra Software 18 The Problem Solving Scheme 19 Strategies to Set up Simple Models 20 Mixture Problem 24 Tank Labeling Problem 27 Linear Programming 30 Modeling a Black Box System 31 Even More Definitions 34 Phenomenological and Mechanistic Models 34 Stationary and Instationary models 38 Distributed and Lumped models 38Classification of Mathematical Models 39 From Black to White Box Models 40 SQM Space Classification: S Axis 41 SQM Space Classification: Q Axis 42

VI

Contents

1.7.4 1.8 2 2.1 2.1.1 2.1.1.1 2.1.1.2 2.1.2 2.1.2.1 2.1.2.2 2.1.2.3 2.1.2.4 2.1.2.5 2.1.2.6 2.1.2.7 2.1.3 2.1.3.1 2.1.3.2 2.1.3.3 2.1.3.4 2.1.3.5 2.2 2.2.1 2.2.2 2.2.3 2.2.4 2.2.5 2.2.6 2.3 2.3.1 2.3.2 2.3.3 2.4 2.4.1 2.4.2 2.4.3 2.4.4...