a numrical method for solving a parabolic problem emanating in financial mathematics

This study aims to develop a robust numerical algorithm for solving parabolic partial differential equations (pdes) arising in the domain of financial mathematics. the proposed approach leverages the finite difference method (fdm) to discretize the temporal and spatial domains of the problem. to approximate the unknown solution, we employ a polynomial interpolation technique, ensuring high accuracy and stability in the numerical solution. the effectiveness and efficiency of our method are demonstrated through comprehensive numerical experiments, showcasing its potential for practical applications in financial modeling.