Modeling of solitary waves via higher-order predictor-corrector scheme

The combination of the sextic b-spline collocation method and the predictor-corrector method is employed to discretize the Regularized Long Wave Equation (RLWE) fully into two systems of linear algebraic equations. Solution of the predictor method is substituted into the corrector method to obtain the unknown which are parameters of the B-spline collocation approach. The property of the new numerical method is demonstrated by studying the propagation of the solitary wave to the left and the interaction of two positive solitary waves.