Overview
- Steps of scientific computing, physical & mathematical description & discussion of numerical results
- Range of applications from different scientific fields; provides complementary bibliography & study guides
- Matlab solutions are provided with the book (GIT repository specified in Preface)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
About this book
This book provides fifteen computational projects aimed at numerically solving problems from a broad range of applications including Fluid Mechanics, Chemistry, Elasticity, Thermal Science, Computer Aided Design, Signal and Image Processing. For each project the reader is guided through the typical steps of scientific computing from physical and mathematical description of the problem to numerical formulation and programming and finally to critical discussion of numerical results. Considerable emphasis is placed on practical issues of computational methods. The last section of each project contains the solutions to all proposed exercises and guides the reader in using the MATLAB scripts. The mathematical framework provides a basic foundation in numerical analysis of partial differential equations and main discretization techniques, such as finite differences, finite elements, spectral methods and wavelets.
The book is primarily intended as a graduate-level textin applied mathematics, but it may also be used by students in engineering or physical sciences. It will also be a useful reference for researchers and practicing engineers.
The second edition builds upon its earlier material (revised and updated) with three all-new chapters intended to reinforce the presentation of mathematical aspects on numerical methods: Fourier approximation, high-order finite difference methods, and basic tools for numerical optimization. Corresponding new applications and programs concern spectral Fourier methods to solve ordinary differential equations, finite difference methods up to sixth-order to solve boundary value problems and, finally, optimization strategies to fit parameters of an epidemiological model.
Keywords
Table of contents (15 chapters)
-
Front Matter
-
Back Matter
Authors and Affiliations
About the authors
Ionut Danaila is Professor of Applied Mathematics at the University of Rouen Normandy, Laboratoire de mathématiques Raphaël Salem, and former member of Laboratoire Jacques-Louis Lions, Sorbonne Université. He is co-author of two textbooks (in French) on scientific computing and one research monograph (on vortex ring models) for researchers and graduate students. His main research interests are in numerical analysis and modern scientific computing. He developed several numerical codes for applications in fluid mechanics, quantum physics and thermal sciences. Over the last decade, he headed two fundamental research projects on the mathematical modelling and high-performance simulation of quantum systems (Bose-Einstein condensates and superfluid helium).
Pascal Joly, now retired, was Research Scientist at Laboratoire Jacques-Louis Lions, Sorbonne Université and Centre national de la recherche scientifique (CNRS). His main research interests concern efficient algorithms in scientific computing (such as solving large sparse linear systems of equations), coding finite element methods for various industrial applications and exploring the wavelets theory in signal processing. He taught courses on numerical methods in various engineering schools and he is former deputy director of the Master of Sciences and Technology of the Université Pierre et Marie Curie for applied Mathematics.
Sidi-Mahmoud Kaber is Associate Professor of Applied Mathematics at Laboratoire Jacques-Louis Lions, Sorbonne Université. He is co-author of three textbooks in French and one in English on numerical analysis. His main research interests include approximation of singular functions and numerical schemes for parallel computing. He is very engaged in using programming and software in mathematics education.
Marie Postel is Associate Professor of Applied Mathematics at Laboratoire Jacques-Louis Lions, Sorbonne Université. She is co-author of two textbooks (in French) on numerical methods. Her research interests are currently mathematical modeling of biological systems, along with the numerical simulation and calibration of model using experimental data. She has designed several adaptive methods in scientific computing for PDEs using multiresolution analysis. She is currently the head of a master program in engineering mathematics, and teaches numerical methods for ODEs, PDEs and optimization at undergraduate and graduate level.
Bibliographic Information
Book Title: An Introduction to Scientific Computing
Book Subtitle: Fifteen Computational Projects Solved with MATLAB
Authors: Ionut Danaila, Pascal Joly, Sidi Mahmoud Kaber, Marie Postel
DOI: https://doi.org/10.1007/978-3-031-35032-0
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023
Hardcover ISBN: 978-3-031-35031-3Published: 08 November 2023
Softcover ISBN: 978-3-031-35034-4Due: 13 January 2024
eBook ISBN: 978-3-031-35032-0Published: 06 November 2023
Edition Number: 2
Number of Pages: XVIII, 373
Number of Illustrations: 27 b/w illustrations, 110 illustrations in colour
Topics: Applications of Mathematics, Computational Mathematics and Numerical Analysis, Computational Intelligence, Theoretical, Mathematical and Computational Physics, Numerical Analysis