Convergence rates of finite difference schemes for the linear advection and wave equation with rough coefficient
Provides rigorous convergence guarantees for numerical schemes solving PDEs with rough coefficients, relevant to computational mathematics.
Proved convergence rates of explicit finite difference schemes for linear advection and wave equations with Hölder continuous coefficients, showing explicit dependence on coefficient regularity and initial data modulus. Numerical experiments confirm theoretical rates.
We prove convergence rates of explicit finite difference schemes for the linear advection and wave equation in one space dimension with Hölder continuous coefficient. The obtained convergence rates explicitly depend on the Hölder 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.