PROGRAM

1. Scientific python 

    Marília Pires, PhD, University of Évora, Portugal

This practice presents the main features of a free software to solve mathematical equations derived from concrete problems.

This course is done on computer.

• Presentation of python

• Basics (number, characters, function) - Graphics

• Linear and nonlinear systems

2. Finite difference methods for PDE 

    Noppadol Chumchob, PhD, Silpakorn University, Thailand

• Brief overview of ordinary and partial differential equations

• Elliptic PDE: 1D, 2D elliptic problems, Convergence theory 

• Parabolic PDE: 1D heat equation, Stability, Convergence theory for time-dependent problems 

• Image processing-image restoration 

3. Exact solutions of smoothing PDE

    Nabil Bedjaoui, PhD, University of Picardie, France 

• Separation of variables, Fourier series 

• Fourier transform

    Fernando da Costa, PhD, University Aberta, Portugal 

• Convolution

• Image restoration, Filtering

4. Hyperbolic PDE 

    Nabil Bedjaoui, PhD, University of Picardie, France 

• Linear and nonlinear models (transport, waves and optics, dissipation and dispersion)

    Joaquim Correia, PhD, University of Évora, Portugal

• Dynamics of image processing & parabolic-hyperbolic models

• Image denoising and restoration & viscosity solutions, shock capturing

• Characteristics, entropies, viscosity-dispersive solution(s) 

• Curves and signals & metrics, dynamic geometry and scales

5. Computer implementation of PDE

    Youcef Mammeri, PhD HDR, University of Picardie, France

This lecture is dedicated to the implementation of methods presented in the other lectures. This course is done on computer.

• • 1D Finite differences implementation

  • Fast Fourier Transform

  • 2D implementation, Kronecker product

  • Examples of simple image processing

  • Scipy routines for image manipulation.