On the numerical solution of nonlinear Burgers'-type equations using meshless method of lines

被引：33

作者：

Haq, Sirajul ^{[1
]}

Hussain, Arshad ^{[1
]}

Uddin, Marjan ^{[2
]}

机构：

[1] GIK Inst, Fac Engn Sci, Topi 23640, Khyber Pakhtunk, Pakistan

[2] UET, Dept Basic Sci, Peshawar, Pakhtunkhwa, Pakistan

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2012年 / 218卷 / 11期

关键词：

Burgers' equation; Burgers'-Huxley equation; Meshless methods; Method of lines; Radial basis functions; Runge-Kutta method; PARTIAL-DIFFERENTIAL-EQUATIONS; RADIAL BASIS FUNCTIONS; COMPUTATIONAL FLUID-DYNAMICS; ADOMIAN DECOMPOSITION METHOD; DATA APPROXIMATION SCHEME; HUXLEY EQUATION; COLLOCATION METHOD; MULTIQUADRICS; CONVERGENCE;

D O I：

10.1016/j.amc.2011.11.106

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, a meshless method of lines (MMOL) is proposed for the numerical solution of nonlinear Burgers'-type equations. This technique does not require a mesh in the problem domain, and only a set of scattered nodes provided by initial data is required for the solution of the problem using some radial basis functions (RBFs). The scheme is tested for various examples. The results obtained by this method are compared with the exact solutions and some earlier work. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：6280 / 6290

页数：11

共 40 条

[1]

Bateman H., 1915, Mon. Weather Rev., V43, P163

[2] A fourth-order numerical scheme for solving the modified Burgers equation [J].

Bratsos, A. G. .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2010, 60 (05) :1393-1400

[3]

Burgers J.M., 1948, ADV APPL MECH, V1, P171

[4] Exponential convergence and H-c multiquadric collocation method for partial differential equations [J].

Cheng, AHD ;

Golberg, MA ;

Kansa, EJ ;

Zammito, G .

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2003, 19 (05) :571-594

[5] PRODUCT APPROXIMATION FOR NON-LINEAR PROBLEMS IN THE FINITE-ELEMENT METHOD [J].

CHRISTIE, I ;

GRIFFITHS, DF ;

MITCHELL, AR ;

SANZSERNA, JM .

IMA JOURNAL OF NUMERICAL ANALYSIS, 1981, 1 (03) :253-266

[6] B-spline Galerkin methods for numerical solutions of the Burgers' equation [J].

Dag, I ;

Saka, B ;

Boz, A .

APPLIED MATHEMATICS AND COMPUTATION, 2005, 166 (03) :506-522

[7]

Danaf T.E., 1998, THESIS MENOUFIA U

[8] Spectral collocation method and Darvishi's preconditionings to solve the generalized Burgers-Huxley equation [J].

Darvishi, M. T. ;

Kheybari, S. ;

Khani, F. .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2008, 13 (10) :2091-2103

[9] Transport schemes on a sphere using radial basis functions [J].

Flyer, Natasha ;

Wright, Grady B. .

JOURNAL OF COMPUTATIONAL PHYSICS, 2007, 226 (01) :1059-1084

[10] Convergence order estimates of meshless collocation methods using radial basis functions [J].

Franke, C ;

Schaback, R .

ADVANCES IN COMPUTATIONAL MATHEMATICS, 1998, 8 (04) :381-399

← 1 2 3 4 →