Numerical Continuation and Bifurcation in Nonlinear PDEs

Numerical Continuation and Bifurcation in Nonlinear PDEs 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. This book 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.

The book uses MATLAB throughout and also provides examples of the Partial Differential Equation Toolbox.