《非线性发展方程的有限差分方法(英文版)(精)》针对应用科学中的介绍了12个重要的非线性演化方程的有限差分方法的最新研究成果，包括微分方程问题解的守恒性和有界性分析、差分方法的建立、差分解的守恒性和有界性分析、差分解的存在性分析、差分解收敛性的证明、差分格式的求解等内容。建立的差分求解格式包括非线性差分格式和线性化差分格式。12个非线性演化方程如下：Fisher方程、Burgers方程、正则长波方程、Korteweg-deVries方程、Camassa-Holm方程、Schr.dinger方程、Kuramoto-Tsuzuki方程、Zakharov方程、Ginzburg-Landau方程、Cahn-Hilliard方程、外延增长模型方程和相场晶体模型方程。

孙志忠，男，1963年3月生。1984年、1987年在南京大学先后获得学士学位、硕士学位。1990年在中国科学院计算中心（现计算数学与科学工程计算研究所）获得博士学位。1990年至今在东南大学数学系任教。现为教授，博士生导师。1997年开始招收研究生。曾经担任东南大学数学建模队教练11年，荣获“全国数学建模优秀教练员”称号，荣获江苏省高等教育教学成果一等奖，江苏省科学技术奖三等奖，江苏省高校“青蓝工程”中青年学术带头人。

Contents
Preface
About the Authors
1 Difference methods for the Fisher equation
1.1 Introduction
1.2 Notation and lemmas
1.3 Forward Euler difference scheme
1.3.1 Derivation of the difference scheme
1.3.2 Solvability and convergence of the difference scheme
1.4 Backward Euler difference scheme
1.4.1 Derivation of the difference scheme
1.4.2 Existence and convergence of the difference solution
1.5 Crank-Nicolson difference scheme
1.5.1 Derivation of the difference scheme
1.5.2 Existence and convergence of the difference solution
1.6 Fourth-order compact difference scheme
1.6.1 Derivation of the difference scheme
1.6.2 Existence and convergence of difference solution
1.7 Three-level linearized difference scheme
1.7.1 Derivation of the difference scheme
1.7.2 Existence and convergence of the difference solution
1.8 Numerical experiments
1.9 Summary and extension
2 Difference methods for the Burgers’ equation
2.1 Introduction
2.2 Two-level nonlinear difference scheme
2.2.1 Derivation of the difference scheme
2.2.2 Conservation and boundedness of the difference solution
2.2.3 Existence and uniqueness of the difference solution
2.2.4 Convergence of the difference solution
2.3 Three-level linearized difference scheme
2.3.1 Derivation of the difference scheme
2.3.2 Existence and uniqueness of the difference solution
2.3.3 Conservation and boundedness of the difference solution
2.3.4 Convergence of the difference solution
2.4 Hopf-Cole transformation and fourth-order difference scheme
2.4.1 Hopf-Cole transformation
2.4.2 Derivation of the difference scheme
2.4.3 Existence and uniqueness of the difference solution
2.4.4 Convergence of the difference solution
2.4.5 Calculation of the solution of the original problem
2.5 Fourth-order compact two-level nonlinear difference scheme
2.5.1 Derivation of the difference scheme
2.5.2 Conservation and boundedness of the difference solution
2.5.3 Existence and uniqueness of the difference solution
2.5.4 Convergence of the difference solution
2.5.5 Stability of the difference solution
2.6 Numerical experiments
2.7 Summary and extension
3 Difference methods for the regularized long-wave equation
3.1 Introduction
3.2 Two-level nonlinear difference scheme
3.2.1 Derivation of the difference scheme
3.2.2 Existence of the difference solution
3.2.3 Conservation and boundedness of the difference solution
3.2.4 Uniqueness of the difference solution
3.2.5 Convergence of the difference solution
3.3 Three-level linearized difference scheme
3.3.1 Derivation of the difference scheme
3.3.2 Conservation and boundedness of the difference solution
3.3.3 Existence and uniqueness of the difference solution
3.3.4 Convergence of the difference solution
3.4 Numerical experiments
3.5 Summary and extension
4 Difference methods for the Korteweg-de Vries equation
4.1 Introduction
4.2 First-order in space two-level nonlinear difference scheme
4.2.1 Derivation of the difference scheme
4.2.2 Existence of the difference solution
4.2.3 Conservation and boundedness of the difference solution
4.2.4 Convergence of the difference solution
4.3 First-order in space three-level linearized difference scheme
4.3.1 Derivation of the difference scheme
4.3.2 Existence and uniqueness of the difference solution
4.3.3 Conservation and boundedness of the difference solution
4.3.4 Convergence of the difference solution
4.4 Second-order in space two-level nonlinear difference scheme
4.4.1 Derivation of the difference scheme
4.4.2 Existence of the difference solution
4.4.3 Conservation and boundedness of the difference solution
4.4.4 Convergence and uniqu