Modeling and Simulation: An Application-Oriented Introduction (Springer Undergraduate Texts in Mathematics and Technology)

By Stefan Zimmer, Martin Buchholz, Dirk Pflüger

Die Autoren führen auf anschauliche und systematische Weise in die mathematische und informatische Modellierung sowie in die Simulation als universelle Methodik ein. Es geht um Klassen von Modellen und um die Vielfalt an Beschreibungsarten. Aber es geht immer auch darum, wie aus Modellen konkrete Simulationsergebnisse gewonnen werden können. Nach einem kompakten Repetitorium zum benötigten mathematischen Apparat wird das Konzept anhand von Szenarien u. a. aus den Bereichen „Spielen – entscheiden – planen" und „Physik im Rechner" umgesetzt.

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Four. 2 Interpolation and Quadrature.. . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 2. four. three Direct resolution of Linear structures of Equations . . . . . . . . . . 2. four. four new release equipment .. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 17 18 19 19 21 28 29 29 30 36 forty-one forty three forty seven forty seven fifty one fifty nine sixty one ix x Contents 2. five half I 2. four. five traditional Differential Equations . . . . . . .. . . . . . . . . . . . . . . . . . . . 2. four. 6 Partial Differential Equations . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . Interrelationships among instruments and purposes . . . . . . . . . . . . . . . . sixty eight seventy eight eighty three Gaming—Deciding—Planning: A Warm-up for Modeling three video game Theory.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . three. 1 video games in Strategic general Form.. . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . three. 2 video games with no Assumptions at the Opponent .. . . . . . . . . . . . . . . . . . . . three. three reaction Mappings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . three. four Dominant innovations .. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . three. five Nash Equilibria .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . three. 6 combined Strategies.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . three. 7 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . four workforce determination Making. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . ninety nine four. 1 person personal tastes and crew choice Making . . . . . . . . . . . . . . . a hundred four. 2 Examples for selection Making tools . . . . . . .. . . . . . . . . . . . . . . . . . . . 103 four. three stipulations for selection features, Arrow’s Theorem . . . . . . . . . . . . . . . 106 five Scheduling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . five. 1 strategy Scheduling (Deterministic) . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . five. 2 Process-Scheduling (Stochastic).. . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . five. three Job-Shop difficulties .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . five. four extra Scheduling difficulties .. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 111 112 118 124 128 6 Wiener procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 6. 1 From the Bernoulli scan to the traditional Distribution . . . . . . . 6. 2 often dispensed enter Parameters . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 6. three Wiener methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 6. four software: improvement of cash Investments.. . . . . . . . . . . . . . . . . 131 132 134 one hundred thirty five 138 half II 7 87 88 ninety ninety one ninety three ninety four ninety five ninety seven site visitors on Highways and knowledge Highways: as soon as throughout the Simulation Pipeline Macroscopic Simulation of highway site visitors . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 7. 1 version Approach.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 7. 2 Homogeneous site visitors movement . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 7. 2. 1 An preliminary consequence . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 7. 2. 2 speed, stream and Density .. . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 7. 2. three basic Diagram .. . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 7. 2. four version Refinements .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 7. three Inhomogeneous site visitors circulate . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 7. four Simulation of an easy round street . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 7. four. 1 a primary try out . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 7. four. 2 a better Simulation .

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