On the numerical solution of two-dimensional Rosenau-Burgers (RB) equation

被引：14

作者：

Omrani, Khaled ^{[1
]}

Debebria, Hajer ^{[2
]}

Bayarassou, Khedidja ^{[3
]}

机构：

[1] Univ Sousse, Inst Super Sci Appliquees & Technol Sousse, Sousse Ibn Khaldoun 4003, Sousse, Tunisia

[2] Univ Carthage, Ecole Polytech Tunis, Rue El Khawarezmi, La Marsa 2078, Tunisia

[3] Univ Sousse, Ecole Super Sci & Technol Hammam Sousse, 4011 H Sousse,Rue L Abassi, Sousse, Tunisia

来源：

ENGINEERING WITH COMPUTERS | 2022年 / 38卷 / 01期

关键词：

Rosenau-Burgers equation; Finite element method; Semidiscrete scheme; Fully discrete method; Linearized difference scheme; Error estimates; FINITE-DIFFERENCE SCHEME;

D O I：

10.1007/s00366-020-01055-2

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

Our purpose is to solve numerically the nonlinear evolutionary problem called Rosenau-Burgers (RB) equation. First, we have derived error estimates of semidiscrete finite element method for the approximation of the Rosenau-Burgers problem. For a second-order accuracy in time, we propose the Galerkin-Crank-Nicolson fully discrete method. Second, a linearized difference scheme for the Rosenau-Burgers equation is considered. It is proved that the proposed difference scheme is uniquely solvable, and the method is shown to be second-order convergent both in time and space in maximum norm. Finally, some numerical experiments are given to demonstrate the validity and accuracy of our linearized difference scheme.

引用

页码：715 / 726

页数：12

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