Ebook: Numerical Methods for Elliptic and Parabolic Partial Differential Equations
- Tags: Numerical Analysis, Computational Mathematics and Numerical Analysis, Numerical and Computational Methods, Appl.Mathematics/Computational Methods of Engineering
- Series: Texts in Applied Mathematics 44
- Year: 2003
- Publisher: Springer-Verlag New York
- Edition: 1
- Language: English
- pdf
Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in - search and teaching, has led to the establishment of the series Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as nume- cal and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and to encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mat- matical Sciences (AMS) series, which will focus on advanced textbooks and research-level monographs.
This book covers numerical methods for partial differential equations: discretization methods such as finite difference, finite volume and finite element methods; solution methods for linear and nonlinear systems of equations and grid generation.
The book takes account of both the theory and implementation, providing simultaneously both a rigorous and an inductive presentation of the technical details. It contains modern topics such as adaptive methods, multilevel methods and methods for convection-dominated problems. Detailed illustrations and extensive exercises are included.
It will provide mathematics students with an introduction to the theory and methods, guiding them in their selection of methods and helping them to understand and pursue finite element programming. For engineering and physics students it will provide a general framework for formulation and analysis of methods providing a broader perspective to specific applications.
This book covers numerical methods for partial differential equations: discretization methods such as finite difference, finite volume and finite element methods; solution methods for linear and nonlinear systems of equations and grid generation.
The book takes account of both the theory and implementation, providing simultaneously both a rigorous and an inductive presentation of the technical details. It contains modern topics such as adaptive methods, multilevel methods and methods for convection-dominated problems. Detailed illustrations and extensive exercises are included.
It will provide mathematics students with an introduction to the theory and methods, guiding them in their selection of methods and helping them to understand and pursue finite element programming. For engineering and physics students it will provide a general framework for formulation and analysis of methods providing a broader perspective to specific applications.
Content:
Front Matter....Pages i-xv
For Example: Modelling Processes in Porous Media with Differential Equations....Pages 1-18
For the Beginning: The Finite Difference Method for the Poisson Equation....Pages 19-45
The Finite Element Method for the Poisson Equation....Pages 46-91
The Finite Element Method for Linear Elliptic Boundary Value Problems of Second Order....Pages 92-175
Grid Generation and A Posteriori Error Estimation....Pages 176-197
Iterative Methods for Systems of Linear Equations....Pages 198-254
The Finite Volume Method....Pages 255-282
Discretization Methods for Parabolic Initial Boundary Value Problems....Pages 283-341
Iterative Methods for Nonlinear Equations....Pages 342-367
Discretization Methods for Convection-Dominated Problems....Pages 368-389
Back Matter....Pages 390-424
This book covers numerical methods for partial differential equations: discretization methods such as finite difference, finite volume and finite element methods; solution methods for linear and nonlinear systems of equations and grid generation.
The book takes account of both the theory and implementation, providing simultaneously both a rigorous and an inductive presentation of the technical details. It contains modern topics such as adaptive methods, multilevel methods and methods for convection-dominated problems. Detailed illustrations and extensive exercises are included.
It will provide mathematics students with an introduction to the theory and methods, guiding them in their selection of methods and helping them to understand and pursue finite element programming. For engineering and physics students it will provide a general framework for formulation and analysis of methods providing a broader perspective to specific applications.
Content:
Front Matter....Pages i-xv
For Example: Modelling Processes in Porous Media with Differential Equations....Pages 1-18
For the Beginning: The Finite Difference Method for the Poisson Equation....Pages 19-45
The Finite Element Method for the Poisson Equation....Pages 46-91
The Finite Element Method for Linear Elliptic Boundary Value Problems of Second Order....Pages 92-175
Grid Generation and A Posteriori Error Estimation....Pages 176-197
Iterative Methods for Systems of Linear Equations....Pages 198-254
The Finite Volume Method....Pages 255-282
Discretization Methods for Parabolic Initial Boundary Value Problems....Pages 283-341
Iterative Methods for Nonlinear Equations....Pages 342-367
Discretization Methods for Convection-Dominated Problems....Pages 368-389
Back Matter....Pages 390-424
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