Wave Equation Stability

In course

Description

This lecture covers the stability analysis of the finite difference scheme for the wave equation, exploring the concept of clean modes and resonant excitation. It delves into the explicit diagram with 3 levels, eigenmodes, eigenfrequencies, and the von Neumann stability analysis. The instructor demonstrates the stability condition and the possibility of exponential amplitude growth over time.

Instructor

Official source

https://mediaspace.epfl.ch/media/0_dfgj5bcm

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In the mathematical subfield of numerical analysis, numerical stability is a generally desirable property of numerical algorithms. The precise definition of stability depends on the context. One is numerical linear algebra and the other is algorithms for solving ordinary and partial differential equations by discrete approximation. In numerical linear algebra, the principal concern is instabilities caused by proximity to singularities of various kinds, such as very small or nearly colliding eigenvalues.

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