A novel numerical scheme for solving Burgers' equation

被引：42

作者：

Xu, Min ^{[2
]}

Wang, Ren-Hong ^{[3
]}

Zhang, Ji-Hong ^{[3
,4
]}

Fang, Qin ^{[1
]}

机构：

[1] Dalian Univ, Coll Informat, Dalian 116622, Peoples R China

[2] Dalian Univ Technol, State Key Lab Struct Anal Ind Equipment, Dalian 116024, Peoples R China

[3] Dalian Univ Technol, Inst Math Sci, Dalian 116024, Peoples R China

[4] Dalian Jiaotong Univ, Sch Sci, Dalian 116028, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2011年 / 217卷 / 09期

关键词：

Cubic spline quasi-interpolant; Bounded linear map; Multi-node higher order expansion; Burgers' equation; MULTIQUADRIC QUASI-INTERPOLATION; SPECTRAL ELEMENT METHOD; GALERKIN METHODS; ORDER; POLYNOMIALS; SPLINES;

D O I：

10.1016/j.amc.2010.10.050

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we propose a novel numerical scheme for solving Burgers' equation. The scheme is based on a cubic spline quasi-interpolant and multi-node higher order expansion, which make the algorithm simple and easy to implement. The numerical experiments show that the proposed method produces high accurate results. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：4473 / 4482

页数：10

共 38 条

[1] A COLLOCATION SOLUTION FOR BURGERS-EQUATION USING CUBIC B-SPLINE FINITE-ELEMENTS
ALI, AHA
GARDNER, GA
GARDNER, LRT
[J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1992, 100 (03) : 325 - 337
[2] ALI AHA, 1990, 9004 UCNW MATHS
[3] FINITE-ELEMENT METHOD FOR BURGERS EQUATION IN HYDRODYNAMICS
ARMINJON, P
BEAUCHAMP, C
[J]. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 1978, 12 (03) : 415 - 428
[4] Bateman H., 1915, Mon. Weather Rev., V43, P163
[5] Burgers J.M., 1948, ADV APPL MECH, V1, P171
[6] Burgers J.M., 1939, Verh. Nederl. Akad. Wetensch. Afd. Natuurk. Sect, V17, P1
[7] Cadwell J, 1987, NUMERICAL METHODS NO
[8] Applying multiquadric quasi-interpolation to solve Burgers' equation
Chen, RH
Wu, ZM
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2006, 172 (01) : 472 - 484
[9] Solving partial differential equation by using multiquadric quasi-interpolation
Chen, Ronghua
Wu, Zongmin
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2007, 186 (02) : 1502 - 1510
[10] UPWINDING OF HIGH-ORDER GALERKIN METHODS IN CONDUCTION-CONVECTION PROBLEMS
CHRISTIE, I
MITCHELL, AR
[J]. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 1978, 12 (11) : 1764 - 1771

← 1 2 3 4 →