AENO: a Novel Reconstruction Method in Conjunction with ADER Schemes for Hyperbolic Equations

Abstract In this paper, we present a novel spatial reconstruction scheme, called AENO , that results from special averaging of the ENO polynomial and its closest neighbour, while retaining stencil direction decided by choice. A variant m-AENO, modified (m-ENO) neighbour. The concept is thoroughly assessed for one-dimensional linear advection equation non-linear hyperbolic system, in conjunction with fully discrete, high-order ADER approach implemented up to fifth order accuracy both space time. results, as compared conventional ENO, m-ENO WENO schemes, are very encouraging. Surprisingly, our show $$L_{1}$$ L 1 -errors smallest most cases considered. Crucially, chosen error size, turns out be efficient method all five methods tested.