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High order finite difference schemes on non-uniform meshes for the time-fractional Black-Scholes equation (1604.05178v1)
Published 18 Apr 2016 in q-fin.CP and cs.CE
Abstract: We construct a three-point compact finite difference scheme on a non-uniform mesh for the time-fractional Black-Scholes equation. We show that for special graded meshes used in finance, the Tavella-Randall and the quadratic meshes the numerical solution has a fourth-order accuracy in space. Numerical experiments are discussed.