The Stability and Convergence of The Numerical Computation for the Temporal Fractional Black-Scholes Equation.

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 τ^2-α order accuracy. Then, the full scheme is collected by approximating the spatial derivative terms with the help of the Chebyshev collocation system focused on the fourth form. Finally, the unconditional stability and convergence order are evaluated by performing the energy process. As an implementation of this method, two examples of the TFBSM were reported to demonstrate the accuracy of the developed scheme. Simulation and comparison show that the suggested strategy is very accurate and effective. [ABSTRACT FROM AUTHOR]