On rate of convergence of finite difference scheme for degenerate parabolic-hyperbolic PDE with Levy noise

12/25/2022

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by   Soumya Ranjan Behera, et al.

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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 (Δ x)^1/7, where Δ x is the spatial mesh size.