Collocation solution for RLW equation with septic spline

A collocation solution using the septic splines as a shape function for the regularized long wave (RLW) equation is presented here. A linear stability analysis shows the scheme to be unconditionally stable. Test problems which, migration and interaction of solitary waves, are used to validate our scheme by calculate L2-norm and L∞-norm, and three invariants of motion are evaluates to determine the conservation properties of the algorithm. The numerical scheme is compared with other published methods and shown to be accurate and efficient