Methods of computer simulations

Romuald Kotowski

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ISBN/ISSN:

978-83-01-21379-4

DOI:

Wydawnictwo:

Wydawnictwo Naukowe PWN

Rok wydania:

2021

Liczba stron:

250

XML:ISBN/ISSN:

ONIX MARC21

Bibliografia:

. Methods of computer simulations. Red. Kotowski, Romuald . : Wydawnictwo Naukowe PWN, 2021, 250 s. ISBN 978-83-01-21379-4

Bibliografia refWorks:

RT Book, Whole

SR Electronic(1)

A2 Kotowski, R.

T1 Methods of computer simulations

PB Wydawnictwo Naukowe PWN

YR 2021

SN 978-83-01-21379-4

Bibliografia BibTex:

@Book{ 260842, author = "", editor = "Kotowski, Romuald", title = "Methods of computer simulations", publisher = "Wydawnictwo Naukowe PWN", year = "2021", address = "", isbn = "978-83-01-21379-4" }

Bibliografia endNote:

TY - BOOK

AU -

ED - Kotowski, Romuald

TI - Methods of computer simulations

PB - Wydawnictwo Naukowe PWN

CY -

PY - 2021

SN - 978-83-01-21379-4

ER -

Netografia (standard APA):

. Red. Kotowski, Romuald. Methods of computer simulations [baza danych online] : Wydawnictwo Naukowe PWN, 2021 [dostęp: 25 04 2024]. Dostęp w Ibuk Libra: https://libra.ibuk.pl/reader/methods-of-computer-simulations-romuald-kotowski-260842.

algebra, computer simulations, fractals, calculus, pendulum, cellular automata

Methods of computer simulations by Romuald Kotowski is a handbook intended for students of computer simulation classes conducted in English. What is inside: • mathematical modelling versus computer simulations, • fundamentals of math...

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ISBN/ISSN:

978-83-01-21379-4

DOI:

Wydawnictwo:

Wydawnictwo Naukowe PWN

Rok wydania:

2021

Liczba stron:

250

XML:ISBN/ISSN:

ONIX MARC21

1. Modeling and computer simulations 12
Introduction12
1.1 Modeling vs. simulation16
1.2 Art of modeling18
1.3 Computer in the contemporary world22
2. Numerical solutions of equations - algebra24
2.1 Numerical solving of nonlinear equations24
2.1.1 Bisection method25
2.1.2 Reguła Falsi method27
2.1.3 Newton's method28
2.1.4 Sturm theorem29
2.2 Definitions and examples30
2.3 Numerical solving of systems of linear equations37
2.3.1 Exact methods37
2.3.2 Iterative methods41
2.4 Eigenproblem of the matrix45
3. Numerical solutions of equations - calculus48
3.1 Ordinary differential equations and integrals49
3.2 Difference methods54
3.2.1 One-step methods54
3.2.2 Many-steps methods56
3.2.3 Iterative methods58
3.2.4 Runge-Kutta methods59
3.3 Numerical integration60
3.3.1 Midpoint rule61
3.3.2 Trapezoid rule62
3.3.3 Simpson's rule62
4. Example from physics - pendulum 64
4.1 Pendulum68
4.1.1 Mathematical pendulum68
4.1.2 Physical pendulum75
4.2 Example of physical pendulum - Foucault pendulum77
5. Cellular automata 80
5.1 Fundamentals of cellular automata81
5.2 Game of Life and other configurations83
5.3 Simulation of motion - Flock88
5.4 Percolation90
6. Deterministic chaos 94
6.1 Logistic iteration94
6.2 Attractors97
6.3 Butterfly effect97
7. Mechanics of materiał points and solid bodies102
7.1 Dynamics of materiał points102
7.2 Mechanics of a solid body108
7.3 Kinematics of a solid body109
7.3.1 Motion110
7.3.2 Momentum111
7.3.3 Energy112
7.3.4 Angular momentum113
7.4 Friction114
8. Modeling of planetary systems118
8.1 Solar System119
8.2 Overview of the planets of the Solar System123
8.3 Ancient astronomy128
8.4 Copernicus Solar System130
8.5 Kepler's laws of planetary motion131
8.6 Law of universal gravitation134
8.7 Cosmic velocities135
8.8 Computer simulation of the Solar System136
9. Fabrics 140
9.1 Modeling140
9.1.1 Physical model140
9.1.2 Mathematical model141
9.1.3 Numerical model143
9.2 Computer simulations of a fabric144
10. Markov processes150
10.1 Markov chains and processes151
10.2 Reminders154
10.3 Examples of Markov processes157
11. F'ractals162
11.1 Examples of fractals163
11.2 Constructive fractals164
11.2.1 Cantor set (1883)164
11.2.2 Koch snowflake165
11.2.3 Sierpiński carpets166
11.3 lterative fractals170
11.3.1 Julia sets170
11.3.2 The Mandelbrot set173
11.3.3 Barnsley fern175
11.4 Applications of fractals177
12. Einstein's theory of relativity 180
12.1 Michelson-Morley experiment183
12.2 Galileo transformation187
12.3 Lorentz transformation188
12.4 Satellite Positioning Systems191
13. Linear programming 196
13.1 Standard form of linear programming198
13.2 Analytical method201
13.3 Graphical method204
14. Genetic algorithms 206
14.1 Simple example of the genetic algorithm209
14.2 Evolutionary strategies211
14.3 Genetic-Based Machine Learning Systems214
15. Dislocations in crystals216
15.1 Kinematics of the dislocation motion218
15.2 Computer simulations224
15.3 Results of the computer simulation of MPE228
16. Problems232
List of Figures239
References246

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