Evolution and Mass Decay of a Gaussian Pulse in Time-Fractional Diffusion: An L1-Implicit Scheme Analysis

We apply the L1-implicit finite difference scheme to solve the time-fractional diffusion equation with a Gaussian initial condition. The Caputo fractional derivative of order α ∈ (0,1] is discretized using the L1 approximation on a uniform temporal mesh, while the spatial second derivative is approximated by a central difference scheme. Numerical simulations are performed to study the effect of the fractional order α on the solution profile and to investigate mass conservation properties. The results demonstrate the characteristic subdiffusive behavior and the non-conservation of mass typically observed in fractional diffusion processes.

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