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math.NA2022★ 1 cited
Numerical analysis of a time-stepping method for the Westervelt equation with time-fractional damping
Katherine Baker, Lehel Banjai, Mariya Ptashnyk
We develop a numerical method for the Westervelt equation, an important equation in nonlinear acoustics, in the form where the attenuation is represented by a class of non-local in…
math.AP2022★ 5 cited
Geometric analysis of fast-slow PDEs with fold singularities via Galerkin discretisation
Maximilian Engel, Felix Hummel, Christian Kuehn +3
We study a singularly perturbed fast-slow system of two partial differential equations (PDEs) of reaction-diffusion type on a bounded domain via Galerkin discretisation. We assume…