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    • Keywords


      Rosenau–RLWequation; Strang time-splitting; quintic B-splines; collocation; Runge–Kutta; stability analysis

    • Abstract


      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 givenby 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 andefficiency of the present scheme, amodel problem with an exact solution is taken into consideration and investigated for various values of the parameter p. The error norms $L_2$ and $L_∞$ 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.

    • Author Affiliations



      1. Department of Mathematics, İnönü University, Malatya, Turkey
      2. Department of Mathematics, Ağrı İbrahim Çeçen University, Ağrı, Turkey
    • Dates

  • Pramana – Journal of Physics | News

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