**Description:**

This
book provides an elementary yet comprehensive introduction to the numerical
solution of partial differential equations (PDEs). Used to model important
phenomena, such as the heating of apartments and the behavior of
electromagnetic waves, these equations have applications in engineering and the
life sciences, and most can only be solved approximately using computers.

*Numerical Analysis of Partial Differential Equations
Using Maple and MATLAB* provides detailed descriptions of
the four major classes of discretization methods for PDEs (finite difference
method, finite volume method, spectral method, and finite element method) and
runnable MATLAB® code for each of the discretization methods and
exercises. It also gives self-contained convergence proofs for each method
using the tools and techniques required for the general convergence analysis
but adapted to the simplest setting to keep the presentation clear and
complete.

Contents:

**Preface**

**Chapter 1.
Introduction** • Notation •
ODEs • PDEs • The Heat Equation • The Advection-Reaction-Diffusion Equation •
The Wave Equation • Maxwell’s Equations • Navier–Stokes Equations • Elliptic
Problems • Problems

**Chapter 2. The Finite
Difference Method** • Finite
Differences for the Two-Dimensional Poisson Equation • Convergence Analysis •
More Accurate Approximations • More General Boundary Conditions • More General
Differential Operators • More General, Nonrectangular Domains • Room
Temperature Simulation Using Finite Differences • Concluding Remarks • Problems

**Chapter 3. The Finite
Volume Method** • Finite
Volumes for a General Two-Dimensional Diffusion Equation • Boundary Conditions
• Relation between Finite Volumes and Finite Differences • Finite Volume
Methods Are Not Consistent • Convergence Analysis • Concluding Remarks •
Problems

**Chapter 4. The
Spectral Method** • Spectral
Method Based on Fourier Series • Spectral Method with Discrete Fourier Series •
Convergence Analysis • Spectral Method Based on Chebyshev Polynomials •
Concluding Remarks • Problems

**Chapter 5. The Finite
Element Method** • Strong Form,
Weak or Variational Form, and Minimization • Discretization • More General
Boundary Conditions • Sobolev Spaces • Convergence Analysis • Generalization to
Two Dimensions • Where Are the Finite Elements? • Concluding Remarks • Problems

**Bibliography **

**Index**

About the Authors:

**Martin J. Gander** is a full professor in
mathematics at the University of Geneva. He was previously a postdoctoral
fellow at École Polytechnique and professor of Mathematics at McGill
University. He has held visiting positions at Paris 13, University of Nice,
RICAM, University of Amiens, Xi’an Jiaotong University, Institut National
Polytechnique de Toulouse, University Henri Poincaré, and the CNRS. Professor
Gander held the Pólya Fellowship at Stanford, a TMR Fellowship from the Swiss
National Science Foundation, and an FCAR strategic professorship from Quebec.
Together with Felix Kwok, he won the SIAM 100-Dollar 100-Digit Challenge, and
with Albert Ruehli the best paper award at the 19th IEEE EPEPS conference. His
main research interest is in numerical analysis, specifically parallel
iterative methods for space-time problems.

**Felix Kwok** is an assistant professor
at Hong Kong Baptist University, before which he spent six years at the
University of Geneva. In 2017, he held a visiting position at Université Côte
d’Azur. He was awarded a Canadian Governor General’s Silver Medal for academic
excellence at McGill University and was the recipient of FCAR and NSERC
doctoral fellowships while at Stanford. Together with Martin J. Gander, he won
the SIAM 100-Dollar 100-Digit Challenge, and in 2018 he was the recipient of
the HKBU President’s Award for Outstanding Performance as a Young Researcher.
His research interests are in scientific computing, particularly the numerical
solution of PDEs and its applications in physics and engineering.

Target Audience:

This
book is intended for advanced undergraduate and early graduate students in
numerical analysis and scientific computing and researchers in related fields.
It is appropriate for a course on numerical methods for partial differential
equations. It is suitable for a one-semester course given to students from
mathematics, computationalscience, and engineering.