This study introduces a novel explicit finite difference scheme for the Black-Scholes (BS) model, eliminating the need for far-field boundary conditions in European option pricing. Through progressive domain reduction during time itera- tion, coupled with a Saulyev-type temporal discretization and non-uniform grids for asset variables, the method achieves stability, enabling the application of larger time steps. Its advantages lie in speed, simplicity, and efficiency, particularly beneficial for nonlinear boundary profiles like power options. Standard computational tests validate its superior performance
