Karaagac, B.Esen, A.Owolabi, K. M.Pindza, E.2024-08-042024-08-0420231995-42391995-4247https://doi.org/10.1134/S1995423923030035https://hdl.handle.net/11616/101584This paper considers an effective numerical collocation method for numerical solution of the KdV-Kawahara equation. This numerical method relies on a finite element formulation and spline interpolation with a trigonometric quintic B-spline basis. First, the KdV-Kawahara equation is reduced to a coupled equation via an auxiliary variable of the form v = u(xxx). The collocation method is then applied to the coupled equation together with the forward difference and the Crank-Nicholson formula. This results in a systemof algebraic equations in terms of time variables with the trigonometric quintic B-spline basis. For determination of the error between the numerical and exact solutions, the error norms L-2 and L-infinity are calculated. The results are illustrated by two numerical examples with their graphical representation and comparison with other methods.eninfo:eu-repo/semantics/closedAccessKdV-Kawahara equationcollocation methodtrigonometric quintic B-spline basisstabilityArticle16321622810.1134/S19954239230300352-s2.0-85171884540Q4WOS:001068710000003Q4