Abstract
In this paper, we propose an improvement of the classical compact finite difference (CFD) method by using a proper
orthogonal decomposition (POD) technique for time-fractional diffusion equations
in one- and two-dimensional space.
A reduced CFD method is constructed with lower dimensions such that it maintains the accuracy and
decreases the computational time in comparison with classical CFD method.
Since the solution of time-fractional diffusion equation typically has a weak singularity near the
initial time
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