A phasefield model in two dimensions with both surface energy and kinetic anisotropies is used to simulate dendritic solidification of a pure material from its undercooled melt. Two finite differences methods have been implemented and their stability regions have been compared. Different regimes of dendritic growth have been obtained from simulations, showing a good qualitative agreement with experimental observations. The dependence of the velocity and direction of growth on the system undercooling has been numerically obtained for a specific case.