dt (d) The Black-Scholes equation for a European call C(S,t) can be transformed into the diffu- sion equation au 2x2 using the transformations S=Ee', 1=1 - 2t/o2 and C=Eu(x, t)exp (k 1)x (k+1) + 2 (k+??-) where the constant k = 2r/o2 is determined by the volatility o and the risk free interest rate r. Let a finite difference method be employed for numerical solution of the trans- formed problem. Consider a computational grid used for numerical solution of the diffusion equation in the domain (x+,x+] x [0, Tmar = oT/2]. We set integers N- 0 (IN-1 =N+) and M > 0 and define 8x=xt/N+ (8x=x-/N-) and 8t = 071/M where 8x >0 and 8t > 0) are the grid step size and time step size, respectively. The grid is then the discrete set of points (xi, tj) [x,x+] x [0,0T/2], where x;=i&x for N- Si0 (IN-1 =N+) and M > 0 and define 8x=xt/N+ (8x=x-/N-) and 8t = 071/M where 8x >0 and 8t > 0) are the grid step size and time step size, respectively. The grid is then the discrete set of points (xi, tj) [x,x+] x [0,0T/2], where x;=i&x for N- Si<><>