Numerical Analysis of Partial Differential Equations Using Maple and MATLAB: (Fundamentals of Algorithms)

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. 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.

About the Author :
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.