The aim of this work is to introduce and study basic numerical methods and advanced methods in order to be able to perform scientific computing. The latter refers to the implementation of approaches adapted to the treatment of a scientific problem arising from physics (meteorology, pollution, etc.) or from engineering (structural mechanics, fluid mechanics, signal processing, automatic control, etc.).
This book is split into two parts. The first part discusses how to solve nonlinear equations and differential equations. The second part examines various numerical methods used for solving partial differential equations: finite differences, finite elements, finite volumes and meshless methods.
Each chapter begins with reminders of definitions which are illustrated with numerical examples and graphic representations. At the end of each chapter, the reader is introduced to the various different commands of the Matlab® software that relate to the explored methods. As in many areas, practice plays a key role in understanding and mastering these methods.
Part 1. Solving Equations
1. Solving Nonlinear Equations.
2. Numerically Solving Differential Equations.
Part 2. Solving PDEs
3. Finite Difference Methods.
4. Finite Element Method.
5. Finite Volume Methods.
6. Meshless Methods.
Part 3. Appendices
Bouchaib Radi is Professeur des universités at the Faculty of Science and Technology of the Hassan First University in Morocco and the author or co-author of 15 books. He is a specialist in digital methods and system reliability.
Abdelkhalak El Hami is Professeur des universités at the Institut National des Sciences Appliquées (INSA-Rouen) in France and the author or co-author of more than 25 books. He is director of the Department of Mechanics and is in charge of the Chair of Mechanics at the Normandy Conservatoire National des Arts et Métiers (CNAM) as well as several European educational and research projects. He is a specialist in the resolution and reliability of multiphysics systems.
Table of Contents
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