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A higher order resolvent positive scheme for fractional derivatives on bounded domains

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FD2W01 - Deterministic and stochastic fractional differential equations and jump processes

We develop a finite difference approximation of order α for the α-fractional derivative.The weights of the approximation scheme have the same rate-matrix type properties asthe popular Grünwald scheme. In particular, approximate solutions to fractional diffusionequations preserve positivity. Furthermore, for the approximation of the solutionto the skewed fractional heat equation on a bounded domain the new approximationscheme keeps its order α whereas the order of the Grünwald scheme reduces to orderα − 1, contradicting the convergence rate results by Meerschaert and Tadjeran. Joint work with M.Kovacs and M.Parry

This talk is part of the Isaac Newton Institute Seminar Series series.

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