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Numerical Methods for Delay Differential Equations

Alfredo Bellen and Marino Zennaro

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198506546
eISBN:
9780191709609
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198506546.001.0001
Subject:
Mathematics, Numerical Analysis

The main purpose of the book is to introduce the numerical integration of the Cauchy problem for delay differential equations (DDEs) and of the neutral type. Comparisons between DDEs and ordinary ... More


Stability Analysis of Runge-Kutta Methods For DDEs

Alfredo Bellen and Marino Zennaro

in Numerical Methods for Delay Differential Equations

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198506546
eISBN:
9780191709609
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198506546.003.0010
Subject:
Mathematics, Numerical Analysis

This chapter addresses the stability analysis of numerical methods, mainly Runge-Kutta, with respect to the test equations introduced in Chapter 9. Due to the many-sided stability requirements and ... More


MHD MODELS FOR ONE INDUSTRIAL APPLICATION

Jean-Frédéric Gerbeau, Claude Le Bris, and Tony Lelièvre

in Mathematical Methods for the Magnetohydrodynamics of Liquid Metals

Published in print:
2006
Published Online:
September 2007
ISBN:
9780198566656
eISBN:
9780191718014
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566656.003.0006
Subject:
Mathematics, Mathematical Physics

This chapter is entirely devoted to one industrial application, the simulation of the industrial production of aluminium in electrolytic cells. The simulation of this specific problem has indeed ... More


Linear Stability Analysis

Gary A. Glatzmaier

in Introduction to Modeling Convection in Planets and Stars: Magnetic Field, Density Stratification, Rotation

Published in print:
2013
Published Online:
October 2017
ISBN:
9780691141725
eISBN:
9781400848904
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691141725.003.0003
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter describes a linear stability analysis (that is, solving for the critical Rayleigh number Ra and mode) that allows readers to check their linear codes against the analytic solution. For ... More


INCOMPRESSIBLE FLOW SIMULATIONS: VERIFICATION AND VALIDATION

George Em Karniadakis and Spencer J. Sherwin

in Spectral/hp Element Methods for Computational Fluid Dynamics

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198528692
eISBN:
9780191713491
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528692.003.0009
Subject:
Mathematics, Numerical Analysis

This chapter discusses numerical simulations of the incompressible Navier-Stokes equations. Exact Navier-Stokes solutions are presented that are used as benchmarks to validate new codes and evaluate ... More


A Primer for Dynamical Systems

Kevin S. McCann

in Food Webs (MPB-50)

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691134178
eISBN:
9781400840687
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691134178.003.0002
Subject:
Biology, Ecology

This chapter introduces the reader to some of the main conceptual ideas behind dynamical systems theory from the perspective of an experimentalist. It first considers the qualitative approaches used ... More


Introduction

Wassim M. Haddad and Sergey G. Nersesov

in Stability and Control of Large-Scale Dynamical Systems: A Vector Dissipative Systems Approach

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691153469
eISBN:
9781400842667
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153469.003.0001
Subject:
Mathematics, Applied Mathematics

This book develops a general stability analysis and control design framework for nonlinear large-scale interconnected dynamical systems, with an emphasis on vector Lyapunov function methods and ... More


Conclusion

Wassim M. Haddad and Sergey G. Nersesov

in Stability and Control of Large-Scale Dynamical Systems: A Vector Dissipative Systems Approach

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691153469
eISBN:
9781400842667
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153469.003.0014
Subject:
Mathematics, Applied Mathematics

This book has described a general stability analysis and control design framework for large-scale dynamical systems, with an emphasis on vector Lyapunov function methods, vector dissipativity theory, ... More


Stability of Topological Derivative Based Imaging Functionals

Habib Ammari, Elie Bretin, Josselin Garnier, Hyeonbae Kang, Hyundae Lee, and Abdul Wahab

in Mathematical Methods in Elasticity Imaging

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691165318
eISBN:
9781400866625
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691165318.003.0008
Subject:
Mathematics, Applied Mathematics

This chapter performs a detailed stability analysis of the topological derivative based imaging functionals with respect to medium and measurement noises. It begins with a discussion of the stability ... More


Optimal Control Theory with Applications in Economics

Thomas A. Weber

Published in print:
2011
Published Online:
August 2013
ISBN:
9780262015738
eISBN:
9780262298483
Item type:
book
Publisher:
The MIT Press
DOI:
10.7551/mitpress/9780262015738.001.0001
Subject:
Mathematics, Probability / Statistics

This book bridges optimal control theory and economics, discussing ordinary differential equations (ODEs), optimal control, game theory, and mechanism design in one volume. Technically rigorous and ... More


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