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Sponsored by the Center for Science and Technology Development of the Ministry of Education
Supervised by Ministry of Education of the People's Republic of China
Based on the long wave equation, a new analytical solution is obtained for long waves propagating over a circular island mounted on a flat bottom. The profile of the island is idealized as a power function of the radial distance with arbitrary powers. The solution is found by using the separation of variables and the Frobenius method. A more straightforward way is applied to solve the ordinary differential equation derived from the long wave equation by separation of variables. The newly derived analytical solution is compared with the previous solution obtained by Jung et al.(2010). Excellent agreement is found between the two solutions for the same cases, while the present solution is superior to that of Jung et al.(2010) in the convergence of the series solution in most cases.