Title Numerical Analysis of Partial Differential Equations Using Maple and MATLAB
Subtitle Fundamentals of Algorithms
Author Martin J. Gander, Felix Kwok
ISBN 9781611975307
List price USD 64.00
Price outside India Available on Request
Original price
Binding Paperback
No of pages 162
Book size 178 x 254 mm
Publishing year 2018
Original publisher SIAM - Society for Industrial and Applied Mathematics (Eurospan Group)
Published in India by .
Exclusive distributors Viva Books Private Limited
Sales territory India, Sri Lanka, Bangladesh, Pakistan, Nepal, .
Status New Arrival
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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.

 

 
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