Abstract: A numerical solution of the initial value problem of regularized long-Wave equation (RLW Equation) was made by a Petrov-Galerkin finite elemnte method. The numerical resuts are consistent with the exact solution of propagation of single solitary wave, due to second-order and fourth-order accuracy for the time and spacing variable respectively. For the collision of two solitons, there is a slight oscilatoiy wave trail after their collision, so it doesn't have the quality of soliton strictly.

Key words: R L W equation, Petrov-Galerkin finite element method, solitary wave, soliton