Partial differential equations, multivariate F-transform, Black-Scholes equation, financial modeling.

In this paper, we propose a numerical method based on the F-transform for solving a certain type of partial differential equations (PDEs) with homogeneous Dirichlet boundary conditions and initial conditions. We show how the PDEs, after the application of the Crank-Nicolson scheme for time discretization, can be approximated by a system of linear equations with the direct F-transform components as their variables. The numerical solution of PDEs is obtained by solving the system of linear equations and the application of the inverse F-transform. The proposed method is then adjusted to the three-dimensional boundary value problem.