where   is the thermal di usivity. Its applications are of fundamental importance in most branches of physics and engineering. Black-Scholes NISQ [FJO21; MK22], FTol Num [JLY22b; An+21]. The Black Scholes equation is a PDE which describes the price of the option V (S, t) over time t and price of underlying asset S(t),r is the  force of interest ,   is the annualized drift rate of S, and   is the standard deviation of the stock s returns.