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

Abstract

Two different methods based on radial basis functions (RBFs) for one-dimensional Kawahara equation are presented. In the first one, we use\xa0 MQ-RBF with predictor-corrector scheme.\xa0 Then the statistical tool LOOCV is implemented\xa0 for selecting good value of shape parameter. In the second one a different scheme is constructed for time and\xa0 then the RBF-QR method is implemented.\xa0 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.