Redefined quintic B-spline collocation technique for nonlinear higher order PDEs

The objective of this work is to present a redefined quintic B-spline (QB-spline) collocation technique for nonlinear higher order PDEs. Two types of PDEs, viz., regularized long-wave (RLW) and Rosenau equations, are considered as these equations play a key role in the modeling of various natural phenomena in science and engineering. The time derivative is discretized by the forward difference scheme, while redefined QB-spline functions are used to integrate the spatial derivatives. Rubin–Graves-type linearization process is used to linearize the nonlinear terms. The discretization of the PDEs gives systems of linear equations. The accuracy and efficiency of the method are checked through three examples. It is found that the present method provides better results than earlier methods. The rate of convergence (ROC) of the method is obtained. The stability analysis is also discussed.