In the present paper, we introduce a numerical solution algorithm based
on a Petrov-Galerkin method in which the element shape functions are cubic
B-splines and the weight functions quadratic B-splines . The motion of a single
solitarywave and interaction of two solitarywaves are studied. Accuracy
and efficiency of the proposed method are discussed by computing the numerical
conserved laws and L2 , L¥ error norms. The obtained results show
that the present method is a remarkably successful numerical technique for
solving the modified equal width wave(MEW) equation. A linear stability
analysis of the scheme shows that it is unconditionally stable
