# Computational Partial Differential Equations Using MATLAB

## 1st Edition

Chapman and Hall/CRC

378 pages | 42 B/W Illus.

Hardback: 9781420089042
pub: 2008-10-20
\$130.00
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eBook (VitalSource) : 9780429143465
pub: 2008-10-20
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### Description

This textbook introduces several major numerical methods for solving various partial differential equations (PDEs) in science and engineering, including elliptic, parabolic, and hyperbolic equations. It covers traditional techniques that include the classic finite difference method and the finite element method as well as state-of-the-art numerical methods, such as the high-order compact difference method and the radial basis function meshless method.

Helps Students Better Understand Numerical Methods through Use of MATLAB®

The authors uniquely emphasize both theoretical numerical analysis and practical implementation of the algorithms in MATLAB, making the book useful for students in computational science and engineering. They provide students with simple, clear implementations instead of sophisticated usages of MATLAB functions.

All the Material Needed for a Numerical Analysis Course

Based on the authors’ own courses, the text only requires some knowledge of computer programming, advanced calculus, and difference equations. It includes practical examples, exercises, references, and problems, along with a solutions manual for qualifying instructors. Students can download MATLAB code from www.crcpress.com, enabling them to easily modify or improve the codes to solve their own problems.

### Reviews

The edition can be surely considered as a successful textbook to study advanced numerical methods for partial differential equations.

—Ivan Secrieru (Chisinau), Zentralblatt Math, 1175

Brief Overview of Partial Differential Equations

The parabolic equations

The wave equations

The elliptic equations

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 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

Index

Bibliographical remarks, Exercises, and References appear at the end of each chapter.