The stability and convergence of the numerical computation for the temporal fractional Black–Scholes equation

Abstract

In this paper‎, ‎the temporal fractional Black–Scholes model (TFBSM) is discussed in the limited specific domain which the time derivative of this template‎ ‎is the Caputo fractional function‎. ‎The value variance of the associated fractal transmission method was applied to forecast TFBSM‎. ‎For solving‎, ‎at first the semi-discrete scheme is obtained by using linear interpolation with a temporally $\tau^{2-\alpha}$ order accuracy‎. ‎Then‎, ‎the full scheme is collected by approximating the spatial derivative terms by helping‎ ‎the Chebyshev collocation system focused on the fourth form‎. ‎Finally‎, ‎the unconditional stability and convergence order is evaluated by performing the energy process‎. ‎As an implementation of this method‎, ‎two examples of the‎ ‎TFBSM was reported to demonstrate the accuracy of the developed scheme‎. ‎Calculation simulation and comparison show that the suggested strategy is very accurate and effective.