A linearized finite-difference method for the solution of some mixed concave and convex non-linear problems

被引：6

作者：

Ben Mabrouk, Anouar ^{[1
]}

Ayadi, Mekki ^{[2
]}

机构：

[1] Fac Sci, Dept Math, Computat Math Lab, Monastir 5000, Tunisia

[2] Higher Inst Appl Sci & Technol, Dept Math & Informat, Ibn Khaldoun 4061, Tunisia

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2008年 / 197卷 / 01期

关键词：

NLS equation; finite-difference scheme; stability analysis; consistency; convergence;

D O I：

10.1016/j.amc.2007.07.051

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the present work, a linearized finite-difference scheme is proposed in order to approximate the solution of some non-linear equation characterized by mixed concave and convex non-linearities. It is proved that the scheme is uniquely solvable and convergent. The resulting method is also analyzed for consistency and stability. Some numerical examples illustrating the method described in our work are given. (C) 2007 Elsevier Inc. All rights reserved.

引用

页码：1 / 10

页数：10

共 12 条

[1] Nodal solutions for some nonlinear elliptic equations [J].

Ben Mabrouk, Anouar ;

Ben Mohamed, Mohamed Lakdar .

APPLIED MATHEMATICS AND COMPUTATION, 2007, 186 (01) :589-597

[2]

Ben Mohamed M.L., 2006, FAR E J APPL MATH, V23, P73

[3]

BENMABROUK A, 2005, 1 MED C APPL MATH TU, P23

[4]

Bratsos, 2000, COMMUN APPL ANAL, V4, P133

[5]

Bratsos A.G., 2001, KOREAN J COMPUT APPL, V8, P459

[6] On nonlinear Schrodinger equations [J].

Grillakis, MG .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2000, 25 (9-10) :1827-1844

[7] Global well-posedness, scattering and blow-up for the energy-critical, focusing, non-linear Schrodinger equation in the radial case [J].

Kenig, Carlos E. ;

Merle, Frank .

INVENTIONES MATHEMATICAE, 2006, 166 (03) :645-675

[8] On the blow up phenomenon of the critical nonlinear Schrodinger equation [J].

Keraani, Sahbi .

JOURNAL OF FUNCTIONAL ANALYSIS, 2006, 235 (01) :171-192

[9]

Lamb G.L., 1980, Pure Appl. Math.

[10] Finite difference approximate solutions for a mixed sub-superlinear equation [J].

Mabrouk, Anouar Ben ;

Mohamed, Mohamed Lakdar Ben ;

Omrani, Khaled .

APPLIED MATHEMATICS AND COMPUTATION, 2007, 187 (02) :1007-1016

← 1 2 →