Analysis of a new finite difference/local discontinuous Galerkin method for the fractional Cattaneo equation (Q2413273)

The author presents a new finite difference scheme to approximate the time fractional derivatives defined in the sense of Caputo, and gives a semidiscrete scheme in time with the truncation error \(O((\Delta t)^{3-\alpha})\), where \(\Delta t\) is the time step size. Further, a fully discrete scheme is discussed for the fractional Cattaneo equation in which the space direction is approximated by a local discontinuous Galerkin method. It is obtained that the method is unconditionally stable and convergent with order \(O(h^{k+1}+(\Delta t)^{3-\alpha})\), where \(k\) is the degree of piecewise polynomial. Numerical examples are also given to illustrate the theoretical findings.