Picard-Reproducing Kernel Hilbert Space Method for Solving Generalized Singular Nonlinear Lane-Emden Type Equations

被引：28

作者：

Azarnavid, Babak ^{[1
]}

Parvaneh, Foroud ^{[2
]}

Abbasbandy, Saeid ^{[1
]}

机构：

[1] Imam Khomeini Int Univ, Dept Math, Ghazvin 3414916818, Iran

[2] Islamic Azad Univ, Kermanshah Branch, Dept Sci, Kermanshah, Iran

来源：

MATHEMATICAL MODELLING AND ANALYSIS | 2015年 / 20卷 / 06期

关键词：

reproducing kernel Hilbert space; Picard iteration; error estimate; convergence; singular nonlinear Lane-Emden type equations; BOUNDARY-VALUE-PROBLEMS; DIFFERENTIAL-EQUATIONS; COLLOCATION METHOD;

D O I：

10.3846/13926292.2015.1111953

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

An iterative method is discussed with respect to its effectiveness and capability of solving singular nonlinear Lane-Emden type equations using reproducing kernel Hilbert space method combined with the Picard iteration. Some new error estimates for application of the method are established. We prove the convergence of the combined method. The numerical examples demonstrates a good agreement between numerical results and analytical predictions.

引用

页码：754 / 767

页数：14

共 25 条

[1] A shooting reproducing kernel Hilbert space method for multiple solutions of nonlinear boundary value problems
Abbasbandy, Saeid
Azarnavid, Babak
Alhuthali, Mohammed S.
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2015, 279 : 293 - 305
[2] ON THE SOLUTION OF THE POISSON-BOLTZMANN EQUATION WITH APPLICATION TO THE THEORY OF THERMAL EXPLOSIONS
CHAMBRE, PL
[J]. JOURNAL OF CHEMICAL PHYSICS, 1952, 20 (11) : 1795 - 1797
[3] Chandrasekhar S., 1938, An Introduction to the Study of Stellar Structure
[4] Cui M., 2009, NONLINEAR NUMERICAL
[5] Davis H.T., 1962, Introduction to Nonlinear Differential and Integral Equations
[6] Emden R, 1907, Gaskugeln
[7] Solving singular nonlinear two-point boundary value problems in the reproducing kernel space
Geng, Fazhan
Cui, Minggen
[J]. JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2008, 45 (03) : 631 - 644
[8] Method for solving nonlinear initial value problems by combining homotopy perturbation and reproducing kernel Hilbert space methods
Geng, Fazhan
Cui, Minggen
Zhang, Bo
[J]. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2010, 11 (02) : 637 - 644
[9] Solving a nonlinear system of second order boundary value problems
Geng, Fazhan
Cui, Minggen
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 327 (02) : 1167 - 1181
[10] Gupta V. G., 2009, INT J APPL MATH COMP, V1, P206

← 1 2 3 →