WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 25, 2026
Integration of the Regularised Long Wave Equation via High Order Predictor-Corrector scheme along with Quartic B-spline Finite element
Authors: , ,
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Abstract: 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.
Keywords:
Multistep predictor-corrector method, Adams-Bashforth-Moulton method, Galerkin method, Quartic B-splines, RLWEequation
Pages: 510-518
DOI: 10.37394/23206.2026.25.47