Integration of the Regularised Long Wave Equation via High Order Predictor-Corrector scheme along with Quartic B-spline Finite element

This study, an algorithm for integrating the Regularized Long Wave Equation (RLWE) is developed by combining a predictor–corrector scheme with the quartic B-spline Galerkin method. The algorithm is first formulated using the four-step implicit Adams–Bashforth method as the predictor and the four-step implicit Adams–Moulton method as the corrector for time integration of the RLWE. Subsequently, the quartic B-spline Galerkin method is applied to the semi-discrete form of the RLWE. The implementation of the algorithm yields a system of algebraic equations whose solutions are used to obtain both discrete and functional approximations of the RLWE. Highly accurate results are achieved through the application of higher-order schemes to test problems involving solitary wave propagation and undulation.