Non-linear partial differential equations have been increasingly used to model the price of options in the realistic market setting when transaction costs arising in the hedging of portfolios are taken into account. This paper focuses on finding the numerical solution of the non-linear partial differential equation corresponding to a Bermudan call option price with variable transaction costs for an asset under the information-based framework. The finite difference method is implemented to approximate the option price and its Greeks. Numerical examples are presented and the option prices compared to the closed-form solution of the information-based model and the Black Scholes model with zero transaction costs. The results show that the approximated option prices correspond to the analytical solution of the information-based model but are slightly higher than the prices under Black-Scholes model. These findings validate the finite difference method as an efficient way of approximating the information-based non-linear partial differential equation.