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Partial Differential Equations and Finite Difference Schemes


- Be able to use standard analytical tools to study partial differential
equations (PDE), for direct and variational analysis of problems.
- Classify first- and second order-partial differential equations, and identify the
possible behaviours of solutions for the transport-diffusion problem.
- Use the notions of convergence, consistency and stability, whatever the kind of
- Analyse convergence of finite difference schemes for time-dependent
problems, and be able to build a stability analysis in Fourier space by means of
symbol theory.
Apply these approximation methods to common first- and second-order partial differential
equations, and perform their implementation.

Needed prerequisite

All courses of 3A MIC, especially the ones focusing of numerical analysis, matrix analysis and ordinary differential equations (EDO).Course on mathematical Analysis (GMM4, semester 7).

Form of assessment

The evaluation of outcome prior learning is made as a continuous training during the semester. According ot the teaching, the assessment will be different: as a written exam, an oral exam, a record, a written report, peers review...