Details

Subject(s)

• Differential equations, Nonlinear—Numerical solutions [Browse]

Publisher

• Society for Industrial and Applied Mathematics [Browse]

Series

• Other titles in applied mathematics. [More in this series]
• Other titles in applied mathematics; 174 [More in this series]

Restrictions note

Restricted to subscribers or individual electronic text purchasers.

Summary note

This book provides a hands-on approach to numerical continuation and bifurcation for nonlinear PDEs in 1D, 2D, and 3D. Partial differential equations (PDEs) are the main tool to describe spatially and temporally extended systems in nature. PDEs usually come with parameters, and the study of the parameter dependence of their solutions is an important task. Letting one parameter vary typically yields a branch of solutions, and at special parameter values, new branches may bifurcate. Numerical Continuation and Bifurcation in Nonlinear PDEs provides a concise review of some analytical background and numerical methods, explains the free MATLAB package pde2path by using a large variety of examples, and contains demo codes that can be easily adapted to the reader's given problem. This book will appeal to applied mathematicians and scientists from physics, chemistry, biology, and economics interested in the numerical solution of nonlinear PDEs, particularly the parameter dependence of solutions. It can be used as a supplemental text in courses on nonlinear PDEs and modeling and bifurcation.

Bibliographic references

Includes bibliographical references (pages 341-357) and index.

System details

• Mode of access: World Wide Web.
• System requirements: Adobe Acrobat Reader.

Source of description

Description based on title page of print version.

Contents

• Getting started
• Liapunov-Schmidt reduction and local bifurcations
• Numerics for continuation and bifurcation
• Finite elements
• Setup and overview of pde2path
• Allen-Cahn equations as model problems
• Examples of Hopf bifurcations
• Pattern formation in 4th order equations
• Reaction-diffusion systems
• Problems on curved surfaces
• Applications in optimal control
• Appendix A. pde2path organization.

Show 9 more Contents items

Other format(s)

Also available in print version.

ISBN

1-61197-661-8

Publisher no.

OT174

LCCN

2021011352

OCLC

1248600446

Doi

• 10.1137/1.9781611976618

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