Simulating, Analyzing, and Animating Dynamical Systems

A Guide to XPPAUT for Researchers and Students

Bard Ermentrout (Autor)

Buch | Softcover

304 Seiten

2002
Society for Industrial & Applied Mathematics,U.S. (Verlag)
978-0-89871-506-4 (ISBN)

Titel z.Zt. nicht lieferbar
Versandkostenfrei
Auch auf Rechnung

Artikel merken

Provides sophisticated numerical methods for the fast and accurate solution of a variety of equations, including ordinary differential equations, delay equations, integral equations, functional equations, and some partial differential equations, as well as boundary value problems. It introduces many modeling techniques and methods for analyzing the resulting equations.

Instructors, students, and researchers will all benefit from this book, which demonstrates how to use software tools to simulate and study sets of equations that arise in a variety of applications. Instructors will learn how to use computer software in their differential equations and modeling classes, while students will learn how to create animations of their equations that can be displayed on the World Wide Web. Researchers will be introduced to useful tricks that will allow them to take full advantage of XPPAUT’s capabilities. In addition, readers will learn several concepts from the field of dynamical systems, including chaos theory, how systems depend on parameters, and how simple physical systems can lead to complicated behavior.

XPPAUT is a tool for simulating, animating, and analyzing dynamical systems that evolved from tools developed by the author for studying nonlinear oscillations. XPPAUT offers several advantages over MATLAB, Maple, and Mathematica, including the following:

1) A faster way to numerically solve differential equations and do numerical integration.
2) More flexibility with integration, including interactive integration that allows the user to see the progress of the solution as it is computed.
3) An interface with AUTO, a continuation packae.
4) Simpler syntax for setting up differentiation equations.
5) Free downloading of the source code.

List of Figures
Preface
Chapter 1: Installation
Chapter 2: A Very Brief Tour of XPPAUT
Chapter 3: Writing ODE Files for Differential Equations
Chapter 4: XPPAUT in the Classroom
Chapter 5: More Advanced Differential Equations
Chapter 6: Spatial Problems, PDE’s, and BVP’s
Chapter 7: Using AUTO: Bifurcation and Continuation
Chapter 8: Animation
Chapter 9: Tricks and Advanced Methods
Appendix A: Colors and Linestyles
Appendix B: The Options
Appendix C: Numerical Methods
Appendix D: Structure of ODE Files
Appendix E: Complete Command List
Appendix F: Error Messages
Appendix G: Cheat Sheet
References
Index.

Erscheint lt. Verlag	31.3.2002
Reihe/Serie	Software Environments and Tools
Verlagsort	New York
Sprache	englisch
Maße	152 x 229 mm
Gewicht	540 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Computerprogramme / Computeralgebra
ISBN-10	0-89871-506-7 / 0898715067
ISBN-13	978-0-89871-506-4 / 9780898715064
Zustand	Neuware