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Computational Partial Differential Equations Using MATLAB

Jichun Li and Yi-Tung Chen
Publisher: 
Chapman & Hall/CRC
Publication Date: 
2009
Number of Pages: 
364
Format: 
Hardcover with CDROM
Series: 
Chapman & Hall/CRC Applied Mathematics and Nonlinear Science Series
Price: 
89.95
ISBN: 
9781420089042
Category: 
Textbook
We do not plan to review this book.

 

Brief Overview of Partial Differential Equations
The parabolic equations
The wave equations
The elliptic equations
Differential equations in broader areas
A quick review of numerical methods for PDEs
Finite Difference Methods for Parabolic Equations
Introduction
Theoretical issues: stability, consistence, and convergence
1-D parabolic equations
2-D and 3-D parabolic equations
Numerical examples with MATLAB codes
Finite Difference Methods for Hyperbolic Equations
Introduction
Some basic difference schemes
Dissipation and dispersion errors
Extensions to conservation laws
The second-order hyperbolic PDEs
Numerical examples with MATLAB codes
Finite Difference Methods for Elliptic Equations
Introduction
Numerical solution of linear systems
Error analysis with a maximum principle
Some extensions
Numerical examples with MATLAB codes
High-Order Compact Difference Methods
1-D problems
High-dimensional problems
Other high-order compact schemes
Finite Element Methods: Basic Theory
Introduction to 1-D problems
Introduction to 2-D problems
Abstract finite element theory
Examples of conforming finite element spaces
Examples of nonconforming finite elements
Finite element interpolation theory
Finite element analysis of elliptic problems
Finite element analysis of time-dependent problems
Finite Element Methods: Programming
Finite element method mesh generation
Forming finite element method equations
Calculation of element matrices
Assembly and implementation of boundary conditions
The MATLAB code for P1 element
The MATLAB code for the Q1 element
Mixed Finite Element Methods
An abstract formulation
Mixed methods for elliptic problems
Mixed methods for the Stokes problem
An example MATLAB code for the Stokes problem
Mixed methods for viscous incompressible flows
Finite Element Methods for Electromagnetics
Introduction to Maxwell’s equations
The time-domain finite element method
The frequency-domain finite element method
Maxwell’s equations in dispersive media
Meshless Methods with Radial Basis Functions
Introduction
The radial basis functions 
The MFS-DRM
Kansa’s method
Numerical examples with MATLAB codes
Coupling RBF meshless methods with DDM
Other Meshless Methods
Construction of meshless shape functions
The element-free Galerkin method
The meshless local Petrov–Galerkin method
Answers to Selected Problems 
Index

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