Numerical scheme based on similarity reductions for the regularized long wave equation

Numerical solution based on similarity reductions for partial differential equations used to get the numerical scheme for the regularized long wave (RLW) equation. The similarity reductions for RLW equation are obtained locally on subdomains defined by the classical three-point stencil. The ordinary differential equation, which deduced from the similarity reduction can be linearized, integrated analytically and then obtain the solution. This approch eliminates the difficulties associated with boundary conditions for the similarity reduction over the whole solution domain. Numerical results are obtained for test problem. The computed results using our scheme confirm the accuracy of our scheme.