Local discontinuous Galerkin schemes for an ultrasonic propagation equation with fractional attenuation

The goal of this article is to develop local discontinuous Galerkin (LDG) schemes for solving a time fractional equation describing the ultrasonic wave in homogeneous isotropic porous material. Two novel semi-discrete LDG are designed considered model. constructed by splitting original model into coupled system. first scheme follows traditional method second-order space derivative. second one splits both and derivatives. used spatial discretization. kinds fully discrete presented using Grünwald-Letnikov L1 approximation formulas $ L^2 norm stability convergence analysis carried out schemes. reveals that numerical unconditionally stable with optimal rate. Finally, examples test effectiveness proposed correctness theoretical analysis.