Nonstandard finite difference schemes for the Black-Scholes partial differential equation preserving the positivity property are proposed. Computationally simple schemes are derived by using a nonlocal approximation in the reaction term of the Black-Scholes equation. Unlike the standard methods, the solutions of new proposed schemes are positive and free of the spurious oscillations.

This dissertation offers a new cluster detection method. This method looks at the cluster detection problem from a new perspective. I change the question of “What do real clusters look like?” to the question of “What do spurious clusters look like?” and “How do spurious clusters affect the ability to recover real clusters?” Spurious clusters can be identified from their geographical characteris...

This paper has several contributions. First, we report that long sudden delays during data transfers are not uncommon in the GPRS wireless WAN. Long sudden delays can lead to spurious TCP timeouts and unnecessary retransmissions. Second, we show that the New Reno algorithm increases the penalty of spurious TCP timeouts and that an aggressive TCP retransmission timer may trigger a chain of spuri...