A new conservative high-order accurate difference scheme for the Rosenau equation

Atouani, Noureddine; Omrani, Khaled

doi:10.1080/00036811.2014.987134

Cited by 41 publications

(12 citation statements)

References 47 publications

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“…1 The existence and uniqueness of the solution of Equation ( 1) was first investigated by Park 2 and Barreto et al 3 The numerical solutions of Equation ( 1) have been studied by several researchers. For example, Chung 4 used nonlinear conservative finite difference scheme (FDS), Omrani et al 5 applied three-level FDS, and Atouani and Omrani 6 presented high-order conservative FDS. Apart from these studies, Chung and Ha 7 analyzed Galerkin finite element method (FEM) and calculated the optimal error of approximate solutions.…”

Section: Introductionmentioning

confidence: 99%

Numerical solutions of nonhomogeneous Rosenau type equations by quintic B‐spline collocation method

Özer

Yağmurlu

2022

Math Methods in App Sciences

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In this study, a numerical scheme based on a collocation finite element method using quintic B‐spline functions for getting approximate solutions of nonhomogeneous Rosenau type equations prescribed by initial and boundary conditions is proposed. The numerical scheme is tested on four model problems with known exact solutions. To show how accurate results the proposed scheme produces, the error norms defined by L2 and L∞ are calculated. Additionally, the stability analysis of the scheme is done by means of the von Neuman method.

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Section: Introductionmentioning

confidence: 99%

Numerical solutions of nonhomogeneous Rosenau type equations by quintic B‐spline collocation method

Özer

Yağmurlu

2022

Math Methods in App Sciences

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“…Omrani et al (2008) obtained numerical solutions by three-level finite difference. Atouani & Omrani (2015) obtained the numerical solutions by high-order FEMs. These schemes are conservative and unconditionally stable.…”

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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“…The theoretical studies, on the existence, uniqueness and regularity for the solution of (1.3), have been performed by Park [5]. Various numerical techniques have been used to solve the Rosenau equation [6][7][8][9][10][11][12], particularly including the discontinuous Galerkin method, the C1-conforming finite element method [13], the finite difference method and the orthogonal cubic spline collocation method. More detailed solving processes can be obtained in Refs.…”

Section: Introductionmentioning

confidence: 99%

A conservative numerical scheme for Rosenau-RLW equation based on multiple integral finite volume method

Guo

Zhang

et al. 2019

Bound Value Probl

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A multiple integral finite volume method combined and Lagrange interpolation are applied in this paper to the Rosenau-RLW (RRLW) equation. We construct a two-level implicit fully discrete scheme for the RRLW equation. The numerical scheme has the accuracy of third order in space and second order in time, respectively. The solvability and uniqueness of the numerical solution are shown. We verify that the numerical scheme keeps the original equation characteristic of energy conservation. It is proved that the numerical scheme is convergent in the order of O(τ 2 + h 3) and unconditionally stable. A numerical experiment is given to demonstrate the validity and accuracy of scheme.

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A new conservative high-order accurate difference scheme for the Rosenau equation

Cited by 41 publications

References 47 publications

Numerical solutions of nonhomogeneous Rosenau type equations by quintic B‐spline collocation method

Numerical solutions of nonhomogeneous Rosenau type equations by quintic B‐spline collocation method

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

A conservative numerical scheme for Rosenau-RLW equation based on multiple integral finite volume method

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