On the convergence of operator splitting for the Rosenau–Burgers equation

Zürnacı, Fatma; Seydaoğlu, Muaz

doi:10.1002/num.22354

Cited by 6 publications

(2 citation statements)

References 26 publications

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“…The operator splitting technique is quite instrumental for the convection–diffusion type problems [22, 23]. In particular, the technique is employed for the KdV equation [18], the BO equation [11], the Burgers–Huxley equation [6], Benjamin–Bona–Mahony equation [15], fractional kinetic Fokker–Planck equation [10], and Rosenau–Burgers equation [34].…”

Section: Introductionmentioning

confidence: 99%

Operator splitting for the fractional Korteweg‐de Vries equation

Dutta

Sarkar

2021

Numerical Methods Partial

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Our aim is to analyze operator splitting for the fractional Korteweg‐de Vries (KdV) equation, ut=italicuux+scriptDαux, α∈false[1,2false], where scriptDα=−(−normalΔ)α/2 is a non‐local operator with α∈false[1,2false). Under the appropriate regularity of the initial data, we demonstrate the convergence of approximate solutions obtained by the Godunov and Strang splitting. Obtaining the Lie commutator bound, we show that for the Godunov splitting, first order convergence in L2 is obtained for the initial data in H1+α and in case of the Strang splitting, second order convergence in L2 is obtained by estimating the Lie double commutator for initial data in H1+2α. The obtained rates are expected in comparison with the KdV false(α=2false) case.

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Section: Introductionmentioning

confidence: 99%

Operator splitting for the fractional Korteweg‐de Vries equation

Dutta

Sarkar

2021

Numerical Methods Partial

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“…Piao et al (2016) obtained the numerical solutions by quadratic B-spline Galerkin method. Zürnacı & Seydaoğlu (2019) presented convergence analysis of operator splitting methods to the equation. In Equation (1), if , then it is called the Rosenau-KdV equation.…”

Section: Introductionmentioning

confidence: 99%

Two efficient numerical methods for solving Rosenau-KdV-RLW equation

Özer

2020

KJS publishes peer-review articles in Mathematics, Computer Sci

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In this study, two efficient numerical schemes based on B-spline finite element method (FEM) and time-splitting methods for solving Rosenau-KdV-RLW equation are presented. In the first method, the equation is solved by cubic B-spline Galerkin FEM. For the second method, after splitting Rosenau-KdV-RLW equation in time, it is solved by Strang timesplitting technique using cubic B-spline Galerkin FEM. The differential equation system in the methods is solved by the fourth-order Runge-Kutta method. The stability analysis of the methods is performed. Both methods are applied to an example. The obtained numerical results are compared with some methods available in the literature via the error norms and , convergence rates, and mass and energy conservation constants. The present results are found to be consistent with the compared ones.

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