Abstract
We consider two kinds of efficient numerical methods to solve the three-dimensional evolution equation with weakly singular kernels. The proposed techniques are based on the finite difference/compact difference methods for the spatial discretization and an alternating direction implicit (ADI) algorithm for the time direction, combined with the second-order convolution quadrature (CQ) rule for the Riemann–Liouville (R-L) integral term and the classical L1 formula for the Caputo fractional derivative. The unconditional stability and convergence of the ADI finite difference scheme are proved rigorously. Numerical results are presented to support the theoretical analysis.
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