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We construct a three-point compact finite difference scheme on a non-uniformmesh for the time-fractional Black-Scholes equation. We show that for specialgraded meshes used in finance, the Tavella-Randall and the quadratic meshes thenumerical solution has a fourth-order accuracy in space. Numerical experimentsare discussed.

High order finite difference schemes on non-uniform meshes for the time-fractional Black-Scholes equation