Higher-order accurate compact schemes and analysis for the time-fractional Black-Scholes model

Abstract

This work is focused on the construction of numerical schemes with higherorder accuracy in space and time to solve the time-fractional Black-Scholes model that governs the price of European options. We develop three numerical schemes utilizing the fourth-order Pad´e approximation, a fourth-order Taylor’s compact difference scheme and a fourth-order compact exponential scheme for spatial discretization. We employ L1-2-3 approximation of order 4 − α, 0 < α < 1, to discretize the time-fractional derivative.In addition, the solvability, convergence, and stability of these numerical schemes are established. Numerical experiments are conducted to demonstrate the accuracy of the proposed schemes and validate the theoretical findings. The new proposed schemes offer higher and better accuracy.