High-order compact finite difference and laplace transform method for the solution of time-fractional heat equations with dirchlet and neumann boundary conditions

The work presents a novel coupling of the Laplace Transform and the compact fourth-order finite-difference discretization scheme for the efficient and accurate solution of linear time-fractional nonhomogeneous diffusion equations subject to both Dirichlet and Neumann boundary conditions. A translational transformation of the dependent variable ensures the Caputo derivative is aligned with the Riemann-Louiville fractional derivative. The resulting scheme is computationally efficient and shown to be uniquely solvable in all cases, accurate and convergent to O (x 4) in the spatial domain. The convergence rates in the temporal domain are contour dependent but exhibit geometric convergence. Numer Methods Partial Differential Eq 32: 1184-1199, 2016.