Scientific Computing.

solved with MATLAB.

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.

- Numerical approximation of model partial differential equations
- Nonlinear differential equations. Application to chemical kinetics
- Polynomial approximation
- Solving an advection-diffusion equation by a finite element method
- Solving a differential equation by a spectral method
- Signal processing: multiresolution analysis
- Elasticity: elastic deformation of a thin plate
- Domain decomposition using a Schwarz method
- Geometrical design: Bézier curves and surfaces
- Gas dynamics : Riemann problem and discontinuous solutions. Application to the shock tube problem
- Thermal engineering: optimization of an industrial furnace
- Fluid dynamics: solving the two-dimensional Navier-Stokes equations

**Download the MATLAB programs for each project **

- Numerical approximation of model partial differential equations TGZ format, ZIP format
- Nonlinear differential equations. Application to chemical kinetics TGZ format, ZIP format
- Polynomial approximation TGZ format, ZIP format
- Solving an advection-diffusion equation by a finite element method TGZ format, ZIP format
- Solving a differential equation by a spectral method TGZ format, ZIP format
- Signal processing: multiresolution analysis TGZ format, ZIP format
- Elasticity: elastic deformation of a thin plate TGZ format, ZIP format
- Domain decomposition using a Schwarz method TGZ format, ZIP format
- Geometrical design: Bézier curves and surfaces TGZ format, ZIP format
- Gas dynamics : Riemann problem and discontinuous solutions. Application to the shock tube problem TGZ format, ZIP format
- Thermal engineering: optimization of an industrial furnace TGZ format, ZIP format
- Fluid dynamics: solving the two-dimensional Navier-Stokes equations TGZ format, ZIP format

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