Approximate analytical solution for the Black-Scholes equation by method of lines

The Stochastic Partial Differential Equations are part of a set of non-linear partial differential equations (PDE), which by their random behavior are difficult to solve analytically and numerically; One of them has been known as the Black-Scholes PDE since 1973, which determines the valuation of goods and/or assets called financial options. The development of the present work is to find numerical approximations to the solution of Black-Scholes PDE by the Method of Lines (MOL). The previous was achieved by means of a methodology based on an analytical study of the classic solution of the BlackScholes PDE. Finally, numerical methods and algorithms were applied to the Black Scholes PDE.