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Operator time‐splitting techniques combined with quintic B‐spline collocation method for the generalized Rosenau–KdV equation
Author(s) -
Kutluay Selçuk,
Karta Melike,
Yağmurlu Nuri M.
Publication year - 2019
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22409
Subject(s) - mathematics , quintic function , korteweg–de vries equation , collocation method , collocation (remote sensing) , mathematical analysis , boundary value problem , operator (biology) , b spline , convergence (economics) , nonlinear system , differential equation , ordinary differential equation , biochemistry , chemistry , physics , remote sensing , repressor , economic growth , economics , quantum mechanics , geology , transcription factor , gene
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 ∞ 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.