Overview

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: Presents hands-on approach to numerical continuation and bifurcation for nonlinear PDEs, in 1D, 2D and 3D. ,Provides a concise but sound review of analytical background and numerical methods. Explains the use of the free MATLAB package pde2path via a large variety of examples with ready to use code. Contains demo codes that can be easily adapted to the reader's given problem. This book will be of interest 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 is appropriate for the following courses: Advanced Numerical Analysis, Special Topics on Numerical Analysis, Topics on Data Science, Topics on Numerical Optimization, and Topics on Approximation Theory.

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9781611976601

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Hannes Uecker has worked at the University of Maryland in College Park, University of Karlsruhe, University of Stuttgart, and, since 2007, the Carl von Ossietzky Universität Oldenburg. His research interests are in analysis and numerics for nonlinear PDEs. Since 2011, he has been involved in the development of the numerical continuation and bifurcation package pde2path. He is the author of one previous book and 70 research papers in applied math. ??

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