International Journal of Mathematical Research 2311-7427 2306-2223 10.18488/journal.24.2020.91.1.10 International Journal of Mathematical Research Numerical Solutions of Black-Scholes Model by Du Fort-Frankel FDM and Galerkin WRM International Journal of Mathematical Research International Journal of Mathematical Research 06-2020 2020 06-2020 06-2020 9 1 1 10 27 Nov 2019 03 Feb 2020 The main objective of this paper is to find the approximate solutions of the Black-Scholes (BS) model by two numerical techniques, namely, Du Fort-Frankel finite difference method (DF3DM), and Galerkin weighted residual method (GWRM) for both (call and put) type of European options. Since both DF3DM and GWRM are the most familiar numerical techniques for solving partial differential equations (PDE) of parabolic type, we estimate options prices by using these techniques. For this, we first convert the Black-Scholes model into a modified parabolic PDE, more specifically, in DF3DM, the first temporal vector is calculated by the Crank-Nicolson method using the initial boundary conditions and then the option price is evaluated. On the other hand, in GWRM, we use piecewise modified Legendre polynomials as the basis functions of GWRM which satisfy the homogeneous form of the boundary conditions. We may observe that the results obtained by the present methods converge fast to the exact solutions. In some cases, the present methods give more accurate results than the earlier results obtained by the adomian decomposition method [14]. Finally, all approximate solutions are shown by the graphical and tabular representations.