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This book covers finite difference methods for two-point boundary value problems, elliptic equations, parabolic equations, hyperbolic equations, high-dimensional evolution equations, fractional differential equations, Schrodinger equations, the Burgers equation and the Korteweg-de Vries equation.
The book strives to achieve:
(a) Featured content. The finite difference method is introduced emphatically.
(b) Scattered difficulty. For the finite difference method, authors start from the two-point boundary value problem of ordinary differential equation and introduce the concepts of finite difference method and frequently used analysis techniques, and then apply these concepts and techniques to solve other partial differential equations.
(c) Emphasis on practicability of the finite difference methods. First authors use examples to demonstrate theoretical results, and then ask students to imitate, and finally master the numerical methods.
The book is suitable for advanced undergraduate and beginning graduate students of applied mathematics and engineering.
Table des matières
Finite Di erence Methods for Two-point Boundary Value Problems.- Finite Di erence Methods for Elliptic Equations.- Finite Di erence Methods for Parabolic Equations.- Finite Di erence Methods for Hyperbolic Equations.- Alternative Directional Implicit Methods for High-dimensional Evolution Equations.- Finite Di erence Methods for Fractional Di erential Equations.- Finite Di erence Methods for the Schr¨odinger Equation.- Finite Di erence Methods for the Burgers Equation.- Finite Di erence Methods for the Korteweg-de Vries Equation.- Bibliography.- Index.
A propos de l'auteur
Zhi-Zhong Sun, Professor at the School of Mathematics, Southeast University. Sun was born in March 1963. He received his bachelor and master degree from Nanjing University in 1984 and 1987 respectively, and obtained his PhD from Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences in 1990. He engaged in the finite difference methods for the partial differential equations, especially the nonlinear evolutionary differential equations, fractional order differential equations.
Qifeng Zhang, Associate Professor at the Department of Mathematics, Zhejiang Sci-Tech University. Zhang was born in September 1987. He received his PhD from Huazhong University of Science and Technology in 2014. He visited Ecole Polytechnique Federale de Lausanne in 2020. His research interests are numerical analysis and simulation of nonlinear water wave equations and fractional order differential equations.
Guang-hua Gao, Associate Professor at the College of Science, Nanjing University of Posts and Telecommunications. Gao was born in November 1985. She obtained her PhD from Southeast University in 2012. She visited University of Macau in 2014. Her main research interest is numerical methods for partial differential equations.
Résumé
This book covers finite difference methods for two-point boundary value problems, elliptic equations, parabolic equations, hyperbolic equations, high-dimensional evolution equations, fractional differential equations, Schrodinger equations, the Burgers’ equation and the Korteweg-de Vries equation.
The book strives to achieve:
(a) Featured content. The finite difference method is introduced emphatically.
(b) Scattered difficulty. For the finite difference method, authors start from the two-point boundary value problem of ordinary differential equation and introduce the concepts of finite difference method and frequently used analysis techniques, and then apply these concepts and techniques to solve other partial differential equations.
(c) Emphasis on practicability of the finite difference methods. First authors use examples to demonstrate theoretical results, and then ask students to imitate, and finally master the numerical methods.
The book is suitable for advanced undergraduate and beginning graduate students of applied mathematics and engineering.
