An efficient numerical scheme on nonuniform grids for a normalized time-fractional Black-Scholes equation

초록

We introduce a normalized time-fractional Black-Scholes (TFBS) model. Under this formulation, we develop a finite difference scheme on a nonuniform grid for the normalized TFBS equation. The grid is obtained through a locally optimal point-removal process followed by a two-stage nonlinear fitting step. Fewer grid points are used overall, while accuracy near the strike price is retained. Numerical results indicate a clear reduction in computational effort and demonstrate the suitability of the proposed approach.

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