zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
A new algorithm for solving differential equations of Lane-Emden type. (English) Zbl 1023.65067
Summary: A reliable algorithm is employed to investigate the differential equations of Lane-Emden type. The algorithm rests mainly on the Adomian decomposition method with an alternate framework designed to overcome the difficulty of the singular point. The proposed framework is applied to a generalization of Lane-Emden equations so that it can be used in differential equations of the same type.

MSC:
65L05Initial value problems for ODE (numerical methods)
34A34Nonlinear ODE and systems, general
65L60Finite elements, Rayleigh-Ritz, Galerkin and collocation methods for ODE
85A15Galactic and stellar structure
WorldCat.org
Full Text: DOI
References:
[1] Davis, H. T.: Introduction to nonlinear differential and integral equations. (1962) · Zbl 0106.28904
[2] Chandrasekhar, S.: Introduction to the study of stellar structure. (1967) · Zbl 0149.24301
[3] O.U. Richardson, The Emission of Electricity from Hot Bodies, London, 1921 · Zbl 48.0118.05
[4] Adomian, G.; Rach, R.; Shawagfeh, N. T.: On the analytic solution of Lane--Emden equation. Foundations of phys. Lett. 8, No. 2, 161-181 (1995)
[5] Adomian, G.: Solving frontier problems of physics: the decomposition method. (1994) · Zbl 0802.65122
[6] Wazwaz, A. M.: A first course in integral equations. (1997) · Zbl 0924.45001
[7] Wazwaz, A. M.: A reliable modification of Adomian’s decomposition method. Appl. math. Comput. 102, 77-86 (1999) · Zbl 0928.65083
[8] Wazwaz, A. M.: Analytical approximations and Padé’s approximants for Volterra’s population model. Appl. math. Comput. 100, 13-25 (1999) · Zbl 0953.92026
[9] Wazwaz, A. M.: A new algorithm for calculating Adomian polynomials for nonlinear operators. Appl. math. Comput. 111, 33-51 (2000) · Zbl 1023.65108
[10] Shawagfeh, N. T.: Nonperturbative approximate solution for Lane--Emden equation. J. math. Phys. 34, No. 9, 4364-4369 (1993) · Zbl 0780.34007
[11] Cherrault, Y.: Convergence of Adomian’s method. Kybernotes 18, No. 2, 31-38 (1989) · Zbl 0697.65051
[12] Adomian, G.: Differential coefficients with singular coefficients. Appl. math. Comput. 47, 179-184 (1992) · Zbl 0748.65066