In the present study, the Modified Equal Width (MEW) wave equation is going to be solved numerically by presenting a new technique based on collocation finite element method in which trigonometric cubic B-splines are used as approximate functions. In order to support the present study, three test problems; namely, the motion of a single solitary wave, interaction of two solitary waves and the birth of solitons are studied. The newly obtained results are compared with some of the other published numerical solutions available in the literature. The accuracy of the proposed method is discussed by computing the numerical conserved laws as well as the error norms L₂ and L_{∞}.