Reliable numerical approximation: from continuous structures to discrete ones
Jeudi, 17 Février, 2022 - 17:00 à 18:00
Mathematical modelling of physical or biological systems is sometimes seen as a way to get precise predictions of the behaviour of the system under study. However, one knows that even simple differential equations can not be solved explicitly, and thus, mathematical modelling does not always seem very suited to get explicit quantitative results.
Starting from the previous observation, I will motivate the need to compute numerical approximations of solutions to ODEs and PDEs, and raise some mathematical issues of such process.
Based on a toy model, the heat equation, I will present some needed features of a "good" approximation for dissipative system, and explain how we can design approximation method satisfyng those properties.
If the time allows, I will also discuss other issues related to the "cost" and the efficiency of the numerical methods.
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