Sorbonne Université

Numerical analysis and partial differential equations.

Course coordinator : K. Schratz

The Major degree Numerical Analysis & Partial Differential Equations (ANEDP) is one of the Majors proposed by the Mathematics of Modelling speciality, second year of the Masters in Mathematics and Applications.

The main degree ANEDP aims at educating:

• researchers in applied mathematics (nonlinear analysis and partial derivative equations, numerical analysis and scientific data processing) likely to pursue a career in higher education and research (Universities, CNRS, ECA, INRIA,…) or to take part in the program of high technology in industry,
• high level mathematical engineers understanding all the aspects of modern scientific calculation (from modelling and mathematical analysis to numerical resolution and effective computer implementation) and who intend to work for industrial research departments and in scientific calculation service companies.

The ANEDP Major's key topic is the theoretical and numerical study of modeled problems by linear and nonlinear partial differential equations from various fields such as physics, engineering, chemistry, biology,  economy, as well as methods of scientific computing aiming at the digital simulation of these problems. Scientific computing has become the key element of technological progress. It requires a deep understanding of mathematical modelling, numerical analysis, and computer science. The broad portfolio of courses of the Major allows students to explore and manage the various aspects of these disciplines. The various fields of mathematics concerned are diversified and developing quickly; their development involves an increasing need for mathematicians. One of the goals of this major is to train such mathematicians. The courses offered cover the following fields:

1. The mathematical modelling of many application areas: solid mechanics, fluid mechanics, propagation phenomena (acoustic, seismic, electromagnetism), the treatment of signal and image, finance, chemistry and combustion.
2. Mathematical analysis of linear and nonlinear partial differential equations (existence, unicity and regularity of solutions).
3. Methods of appoximation: finite elements, finite differences, spectral methods, particulate methods, wavelets.
4. computer implementation of these methods and design of scientific computing software.