Partial differential equations and finite difference method - 4MMMEDP6

• Introduction : Mathematical modelling with PDEs.
  I - Generalities on PDEs
  II - The finite difference method.
  Examples. Consistency, stability and convergence.
  III - Elliptic equations : Laplace and Poisson equations, maximum principle, mean value property, n-D finite difference schemes
  IV - Parabolic equations : Diffusion phenomena.
  Analytic solutions, Fourier's method.
  Finite difference schemes (forward, backward, splitting, non linear case). Stability analysis.
  Multi-D case.
  V Hyperbolic equations. Propagation phenomena.
  Transport equation, characteristics, domain of dependence,
  Finite difference schemes.
  Waves equation
  Non linear case: Burgers. Characteristics, discontinuous solutions.

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

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

N1=E1
N2=E2

The exam is given in english only

The course exists in the following branches:

• Curriculum - Math. Modelling, Image & Simulation - Semester 7 (this course is given in english only )

Course ID : 4MMMEDP6
Course language(s):

The course is attached to the following structures:

• Team Analysis-Computational Science

You can find this course among all other courses.

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