Parallelised numeric solutions implicit-explicit domain decomposition

It is known that Black Scholes equation is used to determine the value of an option.The general strategy is to use a change of variables to transform the PDE into one that is more tractable, the diffusion equation. It is solved numerically using a parallelised domain decomposition method. The spatial domain is split among several processors, with data communicated among the processors using MPI. Interface conditions between domains are calculated using one of three possible schemes: two based on finite differences, and one based on a Green's function solution. Interface results are then used as boundary conditions for each domain to solve the diffusion problem in the domain through an implicit Crank-Nicolson method, because it is based on a tridiagonal linear system solution, has a linear time behaviour.