Semi-implicit difference algorithm for solving the Black-Scholes equation with payment of dividend

Black-Scholes equation is the basic equation of option pricing in financial mathematics, it is important to study it's numerical solution in financial market. This paper constructs a new kind of semi-implicit difference scheme (asymmetric difference scheme) for solving Black-Scholes equation with payment of dividend. Secondly, it gives the convergence of scheme. Thirdly, the stability and error estimates are analyzed. Finally, the numerical examples show the feasibility and effectiveness of the scheme; the computational cost of asymmetric scheme is approximately 95% less than Crank-Nicolson scheme. The scheme is better suitable for applying to calculate the option pricing in the demanding high level of instantaneity.