Numerical methods for differential equations in physics - Département de Physique de l'Ecole Normale supérieure

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Numerical methods for differential equations in physics

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Lectures: Guillaume Legendre
Projects supervision: Guillaume Legendre, Léo Touzo, Nehal Mittal
ECTS credits: 6
Language of instruction: English
Keywords: numerical methods, differential equations, discretization, stability
Exam: oral and written

Description

Most physical theories are expressed in the form of partial differential equations, whether in quantum mechanics, solid or fluid mechanics, or plasma physics or astrophysics. With the advent of computers, it became possible to solve these equations and thus to perform virtual experiments with idealized physical and geometric conditions or even otherwise impossible conditions (for example perfectly flat surfaces, no gravity or radial gravity, no noise). In addition, all of the results are accessible, such as complete velocity and temperature fields, as well as all of the forces.
To solve differential equations numerically, they must be transformed into programs using the algorithms of numerical analysis. The most obvious techniques turn out to be unusable: integrat- ing by using a Taylor series leads to explosive growth; solving a linear system does not require inverting the matrix. Aside from the already considerable advantages of following temporal evo- lution, there is also the possibility of treating the equations with other mathematical techniques: one can calculate unstable steady states, eigenvectors or singular vectors. We will present the various methods used to study physical equations, using as examples the Navier-Stokes and Swift-Hohenberg equations.

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Next student seminar :
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Experimental Internship - Undergraduate program
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November 14 - 18, 2022 :
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Contact us - Student support and Graduate School office :
Tél : 01 44 32 35 60
enseignement@phys.ens.fr