Partial differential equations and finite difference method - 4MMMEDPS

Goal(s)

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.

Content(s)

• Introduction : Mathematical modelling with PDEs.
  II - The finite difference method.
  Examples. Consistancy, 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. Introduction to finite volumes.
  Waves equation
  Non linear case: Burgers. Caracteristics, discontinuous solutions.

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