Higher-order stable compact ADI schemes for multi-term time-fractional diffusion-wave equation in two dimensions

Abstract

This article focuses on developing the compact alternating direction implicit (ADI) numerical scheme based on H3N3-2 σ approximation for the two-dimensional multi-term time-fractional diffusion wave equation (TFDWE). The time-dependent multi-term Caputo derivative of order α r ∈ ( 1 , 2 ) in the equation is discretized by the H3N3-2 σ formula [1] at the super-convergence point σ . The fourth-order accuracy in space of the suggested scheme is governed by implementing compact averaging operator in spatial dimensions. To increase the computational efficiency, the ADI method is used, and a comparison with the non-ADI method is provided. Furthermore, the theoretical analysis demonstrates that the scheme is unconditionally stable and converges in the L 2 norm. The results obtained from our scheme are validated using the numerical examples and found to be more efficient in comparison with the existing literature [2] in both time and space. Another comparative study with [3] also shows that the proposed scheme performs better in terms of accuracy in time and is in good agreement with the result in spatial direction. Furthermore to address the issue of singularity near t = 0 for 2D multi-term TFDWE a comopact-ADI scheme on non-uniform mesh is provided. The proposed technique can be implemented to address various issues related to fractional-order models in a variety of scientific and engineering domains.