Polynomial Least Squares Method for Fractional Lane-Emden Equations

被引：11

作者：

Caruntu, Bogdan ^{[1
]}

Bota, Constantin ^{[1
]}

Lapadat, Marioara ^{[1
]}

Pasca, Madalina Sofia ^{[1
,2
]}

机构：

[1] Politehn Univ Timisoara, Dept Math, P Ta Victoriei 2, Timisoara 300006, Romania

[2] West Univ Timisoara, Dept Math, V Parvan Blv 4, Timisoara 300223, Romania

来源：

SYMMETRY-BASEL | 2019年 / 11卷 / 04期

关键词：

Lane-Emden equation; fractional differential equation; approximate analytical solutions; polynomial least squares method;

D O I：

10.3390/sym11040479

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

This paper applies the Polynomial Least Squares Method (PLSM) to the case of fractional Lane-Emden differential equations. PLSM offers an analytical approximate polynomial solution in a straightforward way. A comparison with previously obtained results proves how accurate the method is.

引用

页数：7

共 17 条

[1]

[Anonymous], 2012, Appl Math

[2] Chebyshev operational matrix method for solving multi-order fractional ordinary differential equations [J].

Atabakzadeh, M. H. ;

Akrami, M. H. ;

Erjaee, G. H. .

APPLIED MATHEMATICAL MODELLING, 2013, 37 (20-21) :8903-8911

[3] Analytical approximate solutions for quadratic Riccati differential equation of fractional order using the Polynomial Least Squares Method [J].

Bota, Constantin ;

Caruntu, Bogdan .

CHAOS SOLITONS & FRACTALS, 2017, 102 :339-345

[4] Approximate polynomial solutions of the nonlinear Lane-Emden type equations arising in astrophysics using the squared remainder minimization method [J].

Caruntu, Bogdan ;

Bota, Constantin .

COMPUTER PHYSICS COMMUNICATIONS, 2013, 184 (07) :1643-1648

[5] ON THE FRACTIONAL LANE-EMDEN EQUATION [J].

Davila, Juan ;

Dupaigne, Louis ;

Wei, Juncheng .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2017, 369 (09) :6087-6104

[6]

EMDEN R., 1907, ANWENDUNGEN MECHANIS

[7] ON FINITE MORSE INDEX SOLUTIONS OF HIGHER ORDER FRACTIONAL LANE-EMDEN EQUATIONS [J].

Fazly, Mostafa ;

Wei, Juncheng .

AMERICAN JOURNAL OF MATHEMATICS, 2017, 139 (02) :433-460

[8] Series solutions for polytropes and the isothermal sphere [J].

Hunter, C .

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, 2001, 328 (03) :839-847

[9]

Lane J.H., 1870, The American Journal of Science and Arts, V50, DOI DOI 10.2475/AJS.S2-50.148.57

[10] Approximate analytical solutions of the Lane-Emden equation for a self-gravitating isothermal gas sphere [J].

Mirza, Babur M. .

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, 2009, 395 (04) :2288-2291

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