Fourth-order alternating direction implicit difference scheme to simulate the space-time Riesz tempered fractional diffusion equation
Mostafa Abbaszadeh, Mehdi Dehghan
Abstract
The current paper proposes a new high-order finite difference scheme with low computational complexity to solve the space-time fractional tempered diffusion equation. At the first stage, the time derivative has been approximated by a difference scheme with second-order accuracy. Furthermore, in the next step, a compact operator has been employed to discretize the space derivative with fourth-order accuracy. After deriving the time-discrete scheme, its stability is analysed. So, a suitable term is added to the main difference scheme. By adding this term, we could construct the main ADI scheme. In the final stage, the convergence order of the full-discrete scheme based upon the ADI formulation is proved. The convergence order of the constructed technique is O((hxα)4+(hyβ)4+τ2). The numerical results show the efficiency of the new technique.