In this paper, we develop two finite difference weighted essentially non-oscillatory (WENO) schemes with unequal-sized sub-stencils for solving the Degasperis-Procesi (DP) and $\mu$-Degasperis-Procesi ($\mu$DP) equations, which contain nonlinear high order derivatives, possibly peakon solutions or shock waves. By introducing auxiliary variable(s), rewrite DP equation as a hyperbolic-elliptic sy...

On the idea of mapped WENO scheme, properties mapping methods are analyzed, uncertainties in development investigated, and new piecewise rational mappings proposed. Based on our former understandings, i.e. at endpoints {0, 1} tending to identity mapping, a so-called Cn,m condition is summarized for function development. Uncertainties, i.e., whether pattern would make scheme behave like or ENO, ...

Implicit integration factor (IIF) methods were developed in the literature for solving time-dependent stiff partial differential equations (PDEs). Recently, IIF methods are combined with weighted essentially non-oscillatory (WENO) schemes in [Jiang and Zhang, Journal of Computational Physics, 253 (2013) 368-388] to efficiently solve stiff nonlinear advection-diffusion-reaction equations. The me...

We develop and demonstrate the capability of a high order accurate finite difference weighted essentially non-oscillatory (WENO) solver for the direct numerical simulation of transients for a two space dimensional Boltzmann transport equation (BTE) coupled with the Poisson equation modeling semiconductor devices such as the MESFET and MOSFET. We compare the simulation results with those obtaine...