pdtm approach to solve black scholes equation for powered ml-payoff function

in this paper, the projected differential transform method (pdtm) has been used to solve the black scholes differential equation for powered modified log payoff (ml-payoff) functions, max{s^k ln ( s/k ) , 0} and max{s^k ln (k/s ) , 0}, (k ∈ r+ ∪ {0}). it is the generalization of black scholes model for ml-payoff functions. it can be seen that values from pdtm are quite accurate to the closed form solutions.