An efficient wavelet‐based approximation method for solving nonlinear fractional‐time long wave equations: An operational matrix approach

Abstract

This research paper develops an efficient Gegenbauer wavelet‐based approximation method to solve nonlinear fractional‐time regularized long wave (RLW) equations arising in ocean engineering. The operational matrices of derivatives, as well as the fractional order integration, are engaged in the proposed method. Using the operational matrix method and collocation point, the nonlinear RLW equations are converted into a system of algebraic equations, and these equations are further solved. Some results regarding the error‐bound estimation of this method have been developed. The method's accuracy and efficiency are confirmed by error estimation. The obtained results are compared with other available results and exact solutions. Moreover, the use of Gegenbauer wavelets is found to be a simple, straightforward forward and efficient tool for solving nonlinear PDEs arising in ocean engineering.