zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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)
On using a modified Legendre-spectral method for solving singular IVPs of Lane-Emden type. (English) Zbl 1205.65201
Summary: Approximate solutions of singular initial value problems (IVPs) of the Lane-Emden type in second-order ordinary differential equations (ODEs) are obtained by an improved Legendre-spectral method. The Legendre-Gauss points are used as collocation nodes and Lagrange interpolation is employed in the Volterra term. The results reveal that the method is effective, simple and accurate.
65L05Initial value problems for ODE (numerical methods)
65L60Finite elements, Rayleigh-Ritz, Galerkin and collocation methods for ODE
[1]Chandrasekhar, S.: An introduction to the study of stellar structure, (1967)
[2]Dehghan, M.; Shakeri, F.: Approximate solution of a differential equation arising in astrophysics using the variational iteration method, New astron. 13, 53-59 (2008)
[3]Davis, H. T.: Introduction to nonlinear differential and integral equations, (1962) · Zbl 0106.28904
[4]Bender, C. M.; Milton, K. A.; Pinsky, S. S.; Simmons, L. M.: A new perturbative approach to nonlinear problems, J. math. Phys. 30, 1447-1455 (1989) · Zbl 0684.34008 · doi:10.1063/1.528326
[5]Wazwaz, A. -M.: A new method for solving singular value problems in the second-order ordinary differential equations, Appl. math. Comput. 128, 45-57 (2001) · Zbl 1030.34004 · doi:10.1016/S0096-3003(01)00021-2
[6]Mandelzweig, V. B.; Tabakin, F.: Quasilinearization approach to nonlinear problems in physics with application to nonlinear odes, Comput. phys. Comm. 141, 268-281 (2001) · Zbl 0991.65065 · doi:10.1016/S0010-4655(01)00415-5
[7]Ramos, J. I.: Linearization methods in classical and quantum mechanics, Comput. phys. Comm. 153, 199-208 (2003) · Zbl 1196.81114 · doi:10.1016/S0010-4655(03)00226-1
[8]He, Ji-Huan: Variational approach to the Lane–Emden equation, Appl. math. Comput. 143, 539-541 (2003)
[9]Parand, K.; Shahini, A.; Dehghan, M.: Rational Legendre pseudospectral approach for solving nonlinear differential equations of Lane–Emden type, J. comput. Phys. 228, 8830-8840 (2009) · Zbl 1177.65100 · doi:10.1016/j.jcp.2009.08.029
[10]Parand, K.; Dehghan, M.; Rezaei, A. R.; Ghaderi, S. M.: An approximation algorithm for the solution of the nonlinear Lane–Emden type equations arising in astrophysics using Hermite functions collocation method, Comput. phys. Comm. 181, 1096-1108 (2010) · Zbl 1216.65098 · doi:10.1016/j.cpc.2010.02.018
[11]Ishtiaq, A.; Brunner, H.; Tang, T.: A spectral method for pantograph-type delay differential equations and its convergence analysis, J. comput. Math. 27, 254-265 (2009) · Zbl 1212.65308
[12]Tang, T.; Xu, X.; Cheng, J.: On spectral methods for Volterra type integral equations and the convergence analysis, J. comput. Math. 26, 825-837 (2008) · Zbl 1174.65058
[13]Yildirim, Ahmet; Öziş, Turgut: Solutions of singular ivps of Lane–Emden type by the variational iteration method, Nonlinear anal. 70, 2480-2484 (2009) · Zbl 1162.34005 · doi:10.1016/j.na.2008.03.012
[14]Yildirim, Ahmet; Öziş, Turgut: Solutions of singular ivps of Lane–Emden type by homotopy perturbation method, Phys. lett. A 369, 70-76 (2007) · Zbl 1209.65120 · doi:10.1016/j.physleta.2007.04.072