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In this article, we have studied the convergence behavior of theDirichlet-Neumann waveform relaxation algorithms for time-fractionalsub-diffusion and diffusion wave equations in 1D \& 2D for regular domains,where the dimensionless diffusion coefficient takes different constant valuesin different subdomains. From numerical experiments, we first capture theoptimal relaxation parameters. Using these optimal relaxation parameters, ouranalysis estimates the rate of change of the convergence behavior against thefractional order and time. We have performed our analysis in multiple subdomaincases for both in 1D \& 2D.

Dirichlet-Neumann Waveform Relaxation Algorithm for Time Fractional Diffusion Equation in Heterogeneous Media