Mathematical modeling of shoreline evolution becomes a useful engineering technique for investigating and predicting the evolution of the plan view of the sandy beach. In this paper two numerical schemes for the shoreline evolution in the long-term scale are presented, and comparisons to analytical solution for some cases are presented for a satisfactory level of suitable numerical scheme. Analytical solutions of shoreline evolution for simple configuration are presented under idealized wave

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... dition. Based on the result that backward time centered space scheme more suitable than forward time centered space scheme to simulate shoreline evolution in the long-term scale. Mathematics Subject Classification: 65L12; 93A30; 37M05 Keyword:mathematical modeling, shoreline evolution, long-term scale, backward time centered space, forward time centered space 5166 Subiyanto et al.