An Introduction to
Scientific Computing.Twelve computational projects
solved with MATLAB.Ionut Danaila, Pascal Joly, Sidi Mahmoud Kaber & Marie Postel.
Computational Science and Engineering.
Springer, New York, 2006.
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The book provides twelve computational projects aimed at numerically solving problems selected to cover a broad spectrum of applications, issued from Fluid Mechanics, Chemistry, Elasticity, Thermal Science, Computer Aided Design, Signal and Image Processing, etc. 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. This complete treatment of each project makes the originality of the book.
Considerable emphasis is placed on practical issues of computational methods which are not usually available in basic text-books. Numerical checking of accuracy or stability, choice of boundary conditions, effective solving of linear systems and comparison to exact solutions when available are only a few examples of problems encountered when applying numerical methods.
The last section of each project contains the solutions of all proposed exercises and guides the reader in using the MATLAB scripts available via Internet. Programming techniques, as vectorial programming, memory storage optimization are also addressed. We finally discuss the physical meaning of the obtained results. Complementary references given at the end of each chapter form a guide for further, more specialized, reading.
The text offers two levels of interest. The mathematical framework provides a basic grounding in the subject of numerical analysis of partial differential equations and main discretization techniques (finite differences, finite elements, spectral methods, wavelets). Meanwhile, we hope that the information contained herein and the wide range of topics covered by the book will allow the reader to select the appropriate numerical method to solve his particular problem.
The book is primarily intended as a graduate-level text in 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. Since different possible developments of the projects are suggested, the text can be used to propose assignments at different graduate levels.
Download the MATLAB programs for each project