Solving the Basset equation via Chebyshev collocation and LDG methods

Two different numerical methods are developed to find approximate solutions of a class of linear fractional differential equations (lfdes) appearing in the study of the generalized basset force, when a sphere sinks in a viscous fluid. in the first one, using the chebyshev bases, the collocation points, and the matrix operations, the given lfde reduces to a matrix equation while in the second one, we employ the local discontinuous galerkin (ldg) method, which uses the natural upwind flux yielding a stable discretization. unlike the first method, in the latter method we are able to solve the problem element by element locally and there is no need to solve a full global matrix. the efficiency of the proposed algorithms are shown via some numerical examples.