Convergence rates of finite difference schemes for the linear advection and wave equation with rough coefficient (1607.00525v1)

Abstract: We prove convergence rates of explicit finite difference schemes for the linear advection and wave equation in one space dimension with H\"older continuous coefficient. The obtained convergence rates explicitly depend on the H\"older regularity of the coefficient and the modulus of continuity of the initial data. We compare the theoretically established rates with the experimental rates of a couple of numerical examples.