Lax-Wendroff Approximate Taylor Methods with Fast and Optimized Weighted Essentially Non-oscillatory Reconstructions

The goal of this work is to introduce new families shock-capturing high-order numerical methods for systems conservation laws that combine Fast WENO (FWENO) and Optimal (OWENO) reconstructions with Approximate Taylor the time discretization. FWENO are based on smoothness indicators require a lower number calculations than standard ones. OWENO definition nonlinear weights allows one unconditionally attain optimal order accuracy regardless critical points. update solutions by using expansion in which, instead Cauchy–Kovalevskaya procedure, derivatives computed combining spatial temporal differentiation expansions recursive way. These compared between them against implementations and/or SSP-RK A test cases considered ranging from scalar linear 1d problems 2d.