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In this work, we use two numerical methods in order to solve the Black-Scholes equation with specified initial and boundary conditions.We use a classical finite difference scheme and an unconditionally positive definite scheme. The stability region is obtained in terms of an inequality involving the temporal step size. We compare the results from both methods at some different values of temporal step size by computing L1, L2 and L∞ errors. [ABSTRACT FROM AUTHOR]

In this work, three finite difference methods have been used to solve a three dimensional advection-diffusion equation with given initial and boundary conditions. The three methods are fourth order finite difference method, Crank-Nicolson and Implicit Chapeau Function. We compare the performance of the methods by computing L2 error, L∞ error and some performance indices such as mass distribution ratio (MDR), mass conservation ratio (MCR), total mass and R² which is a measure of total variation in particle distribution. [ABSTRACT FROM AUTHOR]