Convergence of an operator splitting scheme for fractional conservation laws with Levy noise

TL;DR

This paper proves the convergence of an operator splitting scheme for stochastic conservation laws with Levy noise, ensuring the approximate solutions approach the unique entropy solution, supported by numerical examples.

Contribution

It introduces a novel convergence analysis for an operator splitting scheme applied to stochastic fractional conservation laws with Levy noise.

Findings

Convergence of the splitting scheme to the stochastic entropy solution.

Validation through numerical examples.

Extension to fractional and degenerate cases.

Abstract

In this paper, we are concerned with a operator splitting scheme for linear fractional and fractional degenerate stochastic conservation laws driven by multiplicative Levy noise. More specifically, using a variant of classical Kruzkov's doubling of variable approach, we show that the approximate solutions generated by the splitting scheme converges to the unique stochastic entropy solution of the underlying problems.Finally, the convergence analysis is illustrated by several numerical examples.