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    Operator time-splitting techniques combined with quintic B-spline collocation method for the generalized Rosenau-KdV equation
    (Wiley, 2019) Kutluay, Selcuk; Karta, Melike; Yagmurlu, Nuri M.
    In this article, the generalized Rosenau-KdV equation is split into two subequations such that one is linear and the other is nonlinear. The resulting subequations with the prescribed initial and boundary conditions are numerically solved by the first order Lie-Trotter and the second-order Strang time-splitting techniques combined with the quintic B-spline collocation by the help of the fourth order Runge-Kutta (RK-4) method. To show the accuracy and reliability of the proposed techniques, two test problems having exact solutions are considered. The computed error norms L-2 and L-infinity with the conservative properties of the discrete mass Q(t) and energy E(t) are compared with those available in the literature. The convergence orders of both techniques have also been calculated. Moreover, the stability analyses of the numerical schemes are investigated.
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    Strang time-splitting technique for the generalised Rosenau-RLW equation
    (Indian Acad Sciences, 2021) Kutluay, Selcuk; Karta, Melike; Ucar, Yusuf
    In this paper, a numerical scheme based on quintic B-spline collocation method using the Strang splitting technique is presented for solving the generalised Rosenau-regularised long wave (RLW) equation given by appropriate initial-boundary values. For this purpose, firstly the problem is split into two subproblems such that each one includes the derivative in the direction of time. Secondly, each subproblem is reduced to a system of ordinary differential equations (ODEs) using collocation finite-element method with quintic B-splines for spatial integration. Then, the resulting ODEs for time integration are solved using the Strang time-splitting technique with the second order via the usual Runge-Kutta (RK-4) algorithm with the fourth order. To measure the accuracy and efficiency of the present scheme, a model problem with an exact solution is taken into consideration and investigated for various values of the parameter p. The error norms L2 and L infinity together with the invariants of discrete mass Q and discrete energy E have been computed and a comparison is given with other ones found in the literature. The convergence order of the present numerical scheme has also been computed. Furthermore, the stability analysis of the scheme is numerically examined.