The stability and convergence of the numerical computation for the temporal fractional Black–Scholes equation
DOI:
https://doi.org/10.30495/jme.v15i0.1991Keywords:
Temporal fractional Black–Scholes model, Chebyshev polynomials of the fourth kind, Linear interpolation, Collocation method, Unconditional stability, Convergence orderAbstract
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.
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