Convergence of two conservative high-order accurate difference schemes for the generalized Rosenau-Kawahara-RLW equation

被引：22

作者：

Ghiloufi, Ahlem ^{[1
,2
]}

Rahmeni, Mohamed ^{[2
]}

Omrani, Khaled ^{[2
]}

机构：

[1] Taif Univ, Khurmah Univ Coll, Dept Math, At Taif, Saudi Arabia

[2] Univ Sousse, Inst Super Sci Appl & Technol Sousse, Ibn Khaldoun 4003, Sousse, Tunisia

来源：

ENGINEERING WITH COMPUTERS | 2020年 / 36卷 / 02期

关键词：

Rosenau-Kawahara-RLW equation; Nonlinear difference scheme; Linearized difference scheme; Solitary wave solutions; Conservation laws; Fourth-order accuracy; Unique solvability; Convergence; CCD-ADI METHOD; KDV EQUATION; SOLITONS; MODEL; LAWS;

D O I：

10.1007/s00366-019-00719-y

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

In this paper, we present two high-order accurate difference schemes for the generalized Rosenau-Kawahara-RLW equation. The proposed schemes guarantee the conservation of the discrete energy. The unique solvability of the difference solution is proved. A priori error estimates for the numerical solution is derived. Convergence and stability of the difference schemes are proved. The convergence order is O(h4+k2) in the uniform norm is discussed without any restrictions on the mesh sizes. Finally, numerical experiments are carried out to support the theoretical claims.

引用

页码：617 / 632

页数：16

共 29 条

[1] Solitary Wave Solutions for Generalized Rosenau-KdV Equation [J].

Amin, Esfahani .

COMMUNICATIONS IN THEORETICAL PHYSICS, 2011, 55 (03) :396-398

[2] On the convergence of conservative difference schemes for the 2D generalized Rosenau-Korteweg de Vries equation [J].

Atouani, Noureddine ;

Omrani, Khaled .

APPLIED MATHEMATICS AND COMPUTATION, 2015, 250 :832-847

[3] Galerkin finite element method for the Rosenau-RLW equation [J].

Atouani, Noureddine ;

Omrani, Khaled .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2013, 66 (03) :289-303

[4] Bright and dark solitons of the Rosenau-Kawahara equation with power law nonlinearity [J].

Biswas, A. ;

Triki, H. ;

Labidi, M. .

PHYSICS OF WAVE PHENOMENA, 2011, 19 (01) :24-29

[5]

BROWDER F. E., 1965, P S APPL MATH, V17, P24

[6] Fourth-order compact solution of the nonlinear Klein-Gordon equation [J].

Dehghan, Mehdi ;

Mohebbi, Akbar ;

Asgari, Zohreh .

NUMERICAL ALGORITHMS, 2009, 52 (04) :523-540

[7]

Ebadi G, 2013, ROM J PHYS, V58, P3

[8] A new conservative fourth-order accurate difference scheme for solving a model of nonlinear dispersive equations [J].

Ghiloufi, Ahlem ;

Rouatbi, Asma ;

Omrani, Khaled .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2018, 41 (13) :5230-5253

[9] New conservative difference schemes with fourth-order accuracy for some model equation for nonlinear dispersive waves [J].

Ghiloufi, Ahlem ;

Omrani, Khaled .

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2018, 34 (02) :451-500

[10] An unconditionally stable linearized CCD-ADI method for generalized nonlinear Schrodinger equations with variable coefficients in two and three dimensions [J].

He, Dongdong ;

Pan, Kejia .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2017, 73 (11) :2360-2374

← 1 2 3 →