A third-order Energy Stable Weighted Essentially Non–Oscillatory (ESWENO) finite difference scheme developed by Yamaleev and Carpenter (AIAA 2008–2876, 2008) was proven to be stable in the energy norm for both continuous and discontinuous solutions of systems of linear hyperbolic equations. Herein, a systematic approach is presented that enables “energy stable” modifications for existing WENO s...

Article history: Received 18 September 2013 Received in revised form 26 March 2014 Accepted 29 March 2014 Available online 4 April 2014

4 FDM's for u ′ = f (t, u) 105 4.1 Convergence and stability of explicit, one step FDM's for u ′ =

In this paper a space-time fractional wave equation on a finite domain is considered. The time and space fractional derivative are described in the Caputo sense. We propose a finite difference scheme to solve the space-time fractional wave equation. We discuss about stability and convergence of the method and prove that the finite difference scheme is unconditionally stable and convergent with ...

Article history: Received 24 March 2015 Received in revised form 25 September 2015 Accepted 1 November 2015 Available online 4 November 2015

Starting from a high-order local nonreflecting boundary condition (NBC) for single scattering [25], we derive a local NBC for time-dependent multiple scattering problems, which is completely local both in space and time. To do so, we first develop an exterior evaluation formula for a purely outgoing wave field, given its values and those of certain auxiliary functions needed for the local NBC a...