Operator time-splitting techniques combined with quintic B-spline collocation method for the generalized Rosenau-KdV equation


KUTLUAY S. , Karta M., YAĞMURLU N. M.

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, cilt.35, ss.2221-2235, 2019 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 35 Konu: 6
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1002/num.22409
  • Dergi Adı: NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
  • Sayfa Sayıları: ss.2221-2235

Özet

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.