| Numerical Bifurcation Analysis for Reaction-Diffusion Equations 2000 Edition Contributor(s): Mei, Zhen (Author) |
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ISBN: 3540672966 ISBN-13: 9783540672968 Publisher: Springer OUR PRICE: $104.49 Product Type: Hardcover - Other Formats Published: June 2000 Annotation: This book provides the readers numerical tools for a systematic analysis of bifurcation problems in reaction- diffusion equations. Emphasis is put on combination of numerical analysis with bifurcation theory and application to reaction-diffusion equations. Many examples and figures are used to illustrate analysis of bifurcation scenario and implementation of numerical schemes. The reader will have a thorough understanding of numerical bifurcation analysis and the necessary tools for investigating nonlinear phenomena in reaction-diffusion equations. |
| Additional Information |
| BISAC Categories: - Mathematics | Differential Equations - Partial - Mathematics | Number Systems - Mathematics | Mathematical Analysis |
| Dewey: 515.353 |
| LCCN: 00041043 |
| Series: Springer Computational Mathematics |
| Physical Information: 1.07" H x 6.39" W x 9.5" (1.51 lbs) 414 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: Reaction-diffusion equations are typical mathematical models in biology, chemistry and physics. These equations often depend on various parame- ters, e. g. temperature, catalyst and diffusion rate, etc. Moreover, they form normally a nonlinear dissipative system, coupled by reaction among differ- ent substances. The number and stability of solutions of a reaction-diffusion system may change abruptly with variation of the control parameters. Cor- respondingly we see formation of patterns in the system, for example, an onset of convection and waves in the chemical reactions. This kind of phe- nomena is called bifurcation. Nonlinearity in the system makes bifurcation take place constantly in reaction-diffusion processes. Bifurcation in turn in- duces uncertainty in outcome of reactions. Thus analyzing bifurcations is essential for understanding mechanism of pattern formation and nonlinear dynamics of a reaction-diffusion process. However, an analytical bifurcation analysis is possible only for exceptional cases. This book is devoted to nu- merical analysis of bifurcation problems in reaction-diffusion equations. The aim is to pursue a systematic investigation of generic bifurcations and mode interactions of a dass of reaction-diffusion equations. This is realized with a combination of three mathematical approaches: numerical methods for con- tinuation of solution curves and for detection and computation of bifurcation points; effective low dimensional modeling of bifurcation scenario and long time dynamics of reaction-diffusion equations; analysis of bifurcation sce- nario, mode-interactions and impact of boundary conditions. |
