Solution of Kawahara equation using a predictor-corrector and RBF-QR method

Two different methods based on radial basis functions (RBFs) for one-dimensional Kawahara equation are presented. In the first one, we use  MQ-RBF with predictor-corrector scheme.  Then the statistical tool LOOCV is implemented  for selecting good value of shape parameter. In the second one a different scheme is constructed for time and  then the RBF-QR method is implemented.  In the both of two approaches, the Not-a-Knot method is used to improve the accuracy at the boundaries. The purpose of this paper is to devot suitable strategies to obtain more accurate and efficient solutions specially for arising fifth order time-dependent nonlinear equations comparing with the results from the relevant papers.