On rate of convergence of finite difference scheme for degenerate parabolic-hyperbolic PDE with Levy noise
Year: 2022
Type: preprint
Abstract: In this article, we consider a semi discrete finite difference scheme for a degenerate parabolic-hyperbolic PDE driven by Lévy noise in one space dimension. Using bounded variation estimations and a variant of classical Kružkov's doubling of variable approach, we prove that expected value of the $L^1$-difference between the unique entropy solution and approximate solution converges at a rate of $(Δx)^\frac{1}{7}$, where $Δx$ is the spatial mesh size.
Source: arXiv (Cornell University)
Authors: Behera, Soumya Ranjan, Majee, Ananta K.
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4313197232