Accuracy and stability analysis of the modified Lax numerical method in solving the sea waves refraction equation

We analyse the accuracy and stability of the modified Lax numerical method used in solving the two dimensional sea waves refraction equation. The refraction phenomenon on the beach was observed by the fact that waves hit the shore line in perpendicular way. Angles of the incoming waves from offshore keep changing due to the smaller depth of water, and therefore become important to be determined. The accuracy was evaluated by means of the Taylor series expansion and the stability was analysed by the Von Neumann method. The analysis showed that the method is stable for a certain interval although it is only first order accurate.