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Partial differential equations and finite difference method - 4MMMEDP6

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  • Number of hours

    • Lectures : 16.5
    • Tutorials : 16.5
    ECTS : 3.0

Goals

Numerical solutions of Partial Differential Equations are at the center of computational science. The object of this course is to present the main standard PDEs and to give the principles of the finite difference method. Every chapter contains the continuous problem and several discrete algorithms.

Contact Eric BLAYO

Content

  • Introduction : Mathematical modelling with PDEs.
    I - Generalities on PDEs
    II - The finite difference method.
    Examples. Consistency, stability and convergence.
    III - Parabolic equations : Diffusion phenomena.
    Analytic solutions, Fourier's method.
    Finite difference schemes (forward, backward, splitting, non linear case). Stability analysis.
    Multi-D case.
    IV Hyperbolic equations. Propagation phenomena.
    Transport equation, caracteristics, domain of dependance,
    Finite difference schemes.
    Waves equation
    Non linear case: Burgers. Caracteristics, discontinuous solutions.


Prerequisites

Mathematical analysis (normed spaces, elementary Fourier analysis), linear algebra, basic numerical methods.

Tests

An exam at the end of the term (E).



N1=E1
N2=E2

Additional Information

Curriculum->Math. Modelling, Image & Simulation->Semester 7

Bibliography

G. Allaire. Analyse numerique et optimisation. Editions de l’Ecole Polytechnique, 2006.
L. Evans. Partial Differential Equations. Graduate Studies in Mathematics, Vol 19, American Math. Society, 1998.
R. Leveque. Finite difference methods for ordinary and partial differential equations. SIAM, 2007.
B. Mohammadi, JH Saiac. Pratique de l’analyse numerique. Dunod, 2003

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Date of update January 15, 2017

Grenoble INP Institut d'ingénierie Univ. Grenoble Alpes