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Numerical solution of the Rosenau–KdV–RLW equation by operator splitting techniques based on B‐spline collocation method
Author(s) -
Özer Sibel
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.22387
Subject(s) - mathematics , korteweg–de vries equation , quintic function , operator splitting , collocation method , finite element method , b spline , collocation (remote sensing) , operator (biology) , mathematical analysis , fourier series , numerical analysis , differential equation , nonlinear system , ordinary differential equation , biochemistry , chemistry , physics , remote sensing , repressor , quantum mechanics , geology , gene , transcription factor , thermodynamics
In the present study, the operator splitting techniques based on the quintic B‐spline collocation finite element method are presented for calculating the numerical solutions of the Rosenau–KdV–RLW equation. Two test problems having exact solutions have been considered. To demonstrate the efficiency and accuracy of the present methods, the error norms L 2 and L ∞ with the discrete mass Q and energy E conservative properties have been calculated. The results obtained by the method have been compared with the exact solution of each problem and other numerical results in the literature, and also found to be in good agreement with each other. A Fourier stability analysis of each presented method is also investigated.