B-spline method for solving Bratu's problem

被引：98

作者：

Caglar, Hikmet ^{[2
]}

Caglar, Nazan ^{[1
]}

Ozer, Mehmet ^{[3
]}

Valaristos, Antonios ^{[4
]}

Anagnostopoulos, Antonios N. ^{[5
]}

机构：

[1] Istanbul Kultur Univ, Dept Business Adm, TR-34156 Istanbul, Turkey

[2] Istanbul Kultur Univ, Dept Math Comp, TR-34156 Istanbul, Turkey

[3] Istanbul Kultur Univ, Dept Phys, TR-34156 Istanbul, Turkey

[4] Aristotle Univ Thessaloniki, Dept Informat, GR-54124 Thessaloniki, Greece

[5] Aristotle Univ Thessaloniki, Dept Phys, GR-54124 Thessaloniki, Greece

来源：

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS | 2010年 / 87卷 / 08期

关键词：

Bratu's problem; B-spline method; nonlinear boundary value problem; Laplace method; decomposition method;

D O I：

10.1080/00207160802545882

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we propose a B-spline method for solving the one-dimensional Bratu's problem. The numerical approximations to the exact solution are computed and then compared with other existing methods. The effectiveness and accuracy of the B-spline method is verified for different values of the parameter, below its critical value, where two solutions occur.

引用

页码：1885 / 1891

页数：7

共 20 条

[1] [Anonymous], 1978, A Practical Guide to Splines
[2] [Anonymous], 1987, Unconstrained Optimization: Practical Methods of Optimization
[3] Aregbesola Y A. S., 2003, Electronic Journal of Southern African Mathematical Sciences, V3, P1
[4] Boyd J. P., 1986, Journal of Scientific Computing, V1, P183, DOI 10.1007/BF01061392
[5] Chebyshev polynomial expansions for simultaneous approximation of two branches of a function with application to the one-dimensional Bratu equation
Boyd, JP
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2003, 143 (2-3) : 189 - 200
[6] Application of a Mickens finite-difference scheme to the cylindrical Bratu-Gelfand problem
Buckmire, R
[J]. NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2004, 20 (03) : 327 - 337
[7] Investigations of nonstandard, Mickens-type, finite-difference schemes for singular boundary value problems in cylindrical or spherical coordinates
Buckmire, R
[J]. NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2003, 19 (03) : 380 - 398
[8] B-spline solution of non-linear singular boundary value problems arising in physiology
Caglar, Hikmet
Caglar, Nazan
Oezer, Mehmet
[J]. CHAOS SOLITONS & FRACTALS, 2009, 39 (03) : 1232 - 1237
[9] An algorithm for solving boundary value problems
Deeba, E
Khuri, SA
Xie, SS
[J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2000, 159 (02) : 125 - 138
[10] Frank-Kamenetskii D.A, 1955, DIFFUSION HEAT EXCHA

← 1 2 →