Penyelesaian masalah gelombang dispersi taklinear dengan menggunakan metode homotopi

Abstract

Many natural phenomena can be presented in mathematical models, such as the nonlinear Whitham-Broer-Koup (WBK) wave equation. WBK equation describes wave propagation in shallow waters containing dispersion factor. In this paper, WBK equation will be solved by using homotopy method. Homotopy method is an approximated analytical method, which can be used to obtain the solution of nonlinear problems. The results of this study indicate that homotopy method is highly efficient to solve the WBK equation. Errors resulting from this method are very small, so the solution obtained is very close to its exact solution. One special case of WBK equation discussed in this study is Boussinesq equation, which has a wave number of 0.2 and a frequency of 0.04. The wave initially form a single wave, but then it breaks into two waves, each moving in opposite directions at equal speed.