Finite Difference Methods for Nonlinear Evolution Equations
Description
Nonlinear evolution equations are widely used to describe nonlinear phenomena in natural and social sciences. However, they are usually quite difficult to solve in most instances. This book introduces the finite difference methods for solving nonlinear evolution equations. The main numerical analysis tool is the energy method. This book covers the difference methods for the initial-boundary value problems of twelve nonlinear partial differential equations. They are Fisher equation, Burgers' equation, regularized long-wave equation, Korteweg-de Vries equation, Camassa-Holm equation, Schrödinger equation, Kuramoto-Tsuzuki equation, Zakharov equation, Ginzburg-Landau equation, Cahn-Hilliard equation, epitaxial growth model and phase field crystal model. This book is a monograph for the graduate students and science researchers majoring in computational mathematics and applied mathematics. It will be also useful to all researchers in related disciplines.
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Persons
Zhi-Zhong Sun , Southeast University; Qifeng Zhang , Zhejiang Sci-Tech University; Guang-hua Gao , Nanjing University, China.
Content
- Intro
- Preface
- About the Authors
- Contents
- 1 Difference methods for the Fisher equation
- 2 Difference methods for the Burgers' equation
- 3 Difference methods for the regularized long-wave equation
- 4 Difference methods for the Korteweg-de Vries equation
- 5 Difference methods for the Camassa-Holm equation
- 6 Difference methods for the Schrödinger equation
- 7 Difference methods for the Kuramoto-Tsuzuki equation
- 8 Difference methods for the Zakharov equation
- 9 Difference methods for the Ginzburg-Landau equation
- 10 Difference methods for the Cahn-Hilliard equation
- 11 Difference methods for the epitaxial growth model
- 12 Difference methods for the phase field crystal model
- Bibliography
- Index
