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• W2894842918 abstract "This paper develops appropriate boundary conditions for the two-sided fractional diffusion equation, where the usual second derivative in space is replaced by a weighted average of positive (left) and negative (right) fractional derivatives. Mass preserving, reflecting boundary conditions for two-sided fractional diffusion involve a balance of left and right fractional derivatives at the boundary. Stable, consistent explicit and implicit Euler methods are detailed, and steady state solutions are derived. Steady state solutions for two-sided fractional diffusion equations using both Riemann–Liouville and Caputo flux are computed. For Riemann–Liouville flux and reflecting boundary conditions, the steady-state solution is singular at one or both of the end-points. For Caputo flux and reflecting boundary conditions, the steady-state solution is a constant function. Numerical experiments illustrate the convergence of these numerical methods. Finally, the influence of the reflecting boundary on the steady-state behavior subject to both the Riemann–Liouville and Caputo fluxes is discussed." @default.
• W2894842918 created "2018-10-12" @default.
• W2894842918 creator A5017384955 @default.
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• W2894842918 date "2019-01-01" @default.
• W2894842918 modified "2023-10-16" @default.
• W2894842918 title "Boundary conditions for two-sided fractional diffusion" @default.
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• W2894842918 doi "https://doi.org/10.1016/j.jcp.2018.10.010" @default.
• W2894842918 hasPublicationYear "2019" @default.
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