Article history: Received 10 June 2010 Received in revised form 22 February 2011 Accepted 24 February 2011 Available online 1 March 2011

Article history: Received 30 March 2013 Received in revised form 21 July 2013 Accepted 5 February 2014 Available online 14 February 2014

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 ...