High-order filtered schemes for first order time dependent linear and non-linear partial differential equations

This work is based on high-order “filtered scheme”. Recently filtered scheme has been introduced to solve some first order Hamilton-Jacobi equations. In this paper, we aim to solve some linear and non-linear partial differential equations by a high order filtered scheme. The proposed filtered scheme that is not monotone but still satisfies some ϵ-monotone property with a convergence result and with precise error estimate also has been proven. We will present filtration of different schemes for some linear and non-linear partial differential equations in several dimensions.