volatility in the black-scholes equation

Generally, the black-scholes model and its analyses can be presented in several different ways, ranging from the highly theoretical to the very applied approach. in this article, we will show in detail the applied methodology, the calculations and which effects the applied stress will have on the black-scholes option pricing model. one of the aims of nonlinear analysis is to investigate related topics to the analysis of partial differential equations and their applications. to provide for the further development of the black-scholes model and the black-scholes partial differential equation, we study some related problems. for example, we conclude that the number of call options and volatility increases at the same time.