In this research alternating direction explicit (ADE) method is applied for solving Barles and Soner model which is one of the most complete and comprehensive nonlinear Black-Scholes models. Furthermore the accuracy of this method will be compared with other numerical methods such as finite difference methods. Since in solving nonlinear Black-Scholes models by ADE methods we need to solve only some scalar nonlinear equations instead of a full nonlinear system of equations that we should solve in implicit methods, so this method can be a suitable choice for solving such models
