Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Journal of Applied Mathematics and Computing
Erschienen in: Journal of Applied Mathematics and Computing 1-2/2014

01.02.2014 | Original Research

The Adomian decomposition method with Green’s function for solving nonlinear singular boundary value problems

verfasst von: Randhir Singh, Jitendra Kumar

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 1-2/2014

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

In this paper, we present an efficient numerical algorithm for solving a general class of nonlinear singular boundary value problems. This present algorithm is based on the Adomian decomposition method (ADM) and Green’s function. The method depends on constructing Green’s function before establishing the recursive scheme. In contrast to the existing recursive schemes based on ADM, the proposed numerical algorithm avoids solving a sequence of transcendental equations for the undetermined coefficients. The approximate series solution is calculated in the form of series with easily computable components. Moreover, the convergence analysis and error estimation of the proposed method is given. Furthermore, the numerical examples are included to demonstrate the accuracy, applicability, and generality of the proposed scheme. The numerical results reveal that the proposed method is very effective.
Vorheriger Artikel Preconditioning analysis of the one dimensional incremental unknowns method on nonuniform meshes
Nächster Artikel Existence of solutions for nonlinear high-order fractional boundary value problem with integral boundary condition

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren
Anhänge
Nur mit Berechtigung zugänglich
Literatur
1.
2.
3.
Rachunkov’, I., Pulverer, G., Weinmüller, E.: A unified approach to singular problems arising in the membrane theory. Appl. Math. 55(1), 47–75 (2010) CrossRefMathSciNet
4.
Amit, K.V., et al.: On a constructive approach for derivative-dependent singular boundary value problems. Int. J. Differ. Equ. (2011)
5.
Baxley, J.V., Robinson, S.B.: Nonlinear boundary value problems for shallow membrane caps, II. J. Comput. Appl. Math. 88(1), 203–224 (1998) CrossRefMATHMathSciNet
6.
Pandey, R., Verma, A.K.: On solvability of derivative dependent doubly singular boundary value problems. J. Appl. Math. Comput. 33(1–2), 489–511 (2010) CrossRefMATHMathSciNet
7.
Chawla, M., Katti, C.: Finite difference methods and their convergence for a class of singular two point boundary value problems. Numer. Math. 39(3), 341–350 (1982) CrossRefMATHMathSciNet
8.
Kumar, M., Aziz, T.: A uniform mesh finite difference method for a class of singular two-point boundary value problems. Appl. Math. Comput. 180(1), 173–177 (2006) CrossRefMATHMathSciNet
9.
Ravi Kanth, A., Reddy, Y.: Cubic spline for a class of singular two-point boundary value problems. Appl. Math. Comput. 170(2), 733–740 (2005) CrossRefMATHMathSciNet
10.
Kumar, M., Singh, N.: Modified Adomian decomposition method and computer implementation for solving singular boundary value problems arising in various physical problems. Comput. Chem. Eng. 34(11), 1750–1760 (2010) CrossRef
11.
Ebaid, A.: A new analytical and numerical treatment for singular two-point boundary value problems via the Adomian decomposition method. J. Comput. Appl. Math. 235(8), 1914–1924 (2011) CrossRefMATHMathSciNet
12.
Khuri, S., Sayfy, A.: A novel approach for the solution of a class of singular boundary value problems arising in physiology. Math. Comput. Model. 52(3), 626–636 (2010) CrossRefMATHMathSciNet
13.
Danish, M., Kumar, S., Kumar, S.: A note on the solution of singular boundary value problems arising in engineering and applied sciences: use of OHAM. Comput. Chem. Eng. 36, 57–67 (2012) CrossRef
14.
Singh, R., Kumar, J., Nelakanti, G.: New approach for solving a class of doubly singular two-point boundary value problems using Adomian decomposition method. Adv. Numer. Anal. 2012, 22 (2012). doi:10.​1155/​2012/​541083 MathSciNet
15.
Ravi Kanth, A., Aruna, K.: He’s variational iteration method for treating nonlinear singular boundary value problems. Comput. Math. Appl. 60(3), 821–829 (2010) CrossRefMATHMathSciNet
16.
Inc, M., Evans, D.: The decomposition method for solving of a class of singular two-point boundary value problems. Int. J. Comput. Math. 80(7), 869–882 (2003) CrossRefMATHMathSciNet
17.
Wazwaz, A., Rach, R.: Comparison of the Adomian decomposition method and the variational iteration method for solving the Lane-Emden equations of the first and second kinds. Kybernetes 40(9/10), 1305–1318 (2011) CrossRefMathSciNet
18.
Kumar, M., Gupta, Y.: Methods for solving singular boundary value problems using splines: a review. J. Appl. Math. Comput. 32(1), 265–278 (2010) CrossRefMATHMathSciNet
19.
Wazwaz, A.: The variational iteration method for solving nonlinear singular boundary value problems arising in various physical models. Commun. Nonlinear Sci. Numer. Simul. 16(10), 3881–3886 (2011) CrossRefMATH
20.
21.
Benabidallah, M., Cherruault, Y.: Application of the Adomian method for solving a class of boundary problems. Kybernetes 33(1), 118–132 (2004) CrossRefMATHMathSciNet
22.
Adomian, G.: Solving Frontier Problems of Physics: The Decomposition Methoc [ie Method]. Kluwer Academic, Dordrecht (1994) CrossRef
23.
24.
Wazwaz, A.: Approximate solutions to boundary value problems of higher order by the modified decomposition method. Comput. Math. Appl. 40(6), 679–691 (2000) CrossRefMATHMathSciNet
25.
Wazwaz, A.: A reliable algorithm for obtaining positive solutions for nonlinear boundary value problems. Comput. Math. Appl. 41(10–11), 1237–1244 (2001) CrossRefMATHMathSciNet
26.
Haldar, K.: Application of Adomian’s approximation to blood flow through arteries in the presence of a magnetic field. J. Appl. Math. Comput. 12(1–2), 267–279 (2003) CrossRefMATHMathSciNet
27.
Al-Khaled, K., Allan, F.: Decomposition method for solving nonlinear integro-differential equations. J. Appl. Math. Comput. 19(1–2), 415–425 (2005) CrossRefMATHMathSciNet
28.
Momani, S., Moadi, K.: A reliable algorithm for solving fourth-order boundary value problems. J. Appl. Math. Comput. 22(3), 185–197 (2006) CrossRefMATHMathSciNet
29.
El-Kalla, I.: Error estimates for series solutions to a class of nonlinear integral equations of mixed type. J. Appl. Math. Comput. 38(1–2), 341–351 (2012) CrossRefMathSciNet
30.
Mamaloukas, C., Haldar, K., Mazumdar, H.: Application of double decomposition to pulsatile flow. J. Appl. Math. Comput. 10(1–2), 193–207 (2002) CrossRefMATHMathSciNet
31.
El-Sayed, A., Saleh, M., Ziada, E.: Analytical and numerical solution of multi-term nonlinear differential equations of arbitrary orders. J. Appl. Math. Comput. 33(1–2), 375–388 (2010) CrossRefMATHMathSciNet
32.
Wazwaz, A.M., Rach, R., Duan, J.-S.: Adomian decomposition method for solving the Volterra integral form of the Lane–Emden equations with initial values and boundary conditions. Appl. Math. Comput. 219(10), 5004–5019 (2013) CrossRefMathSciNet
33.
Al-Hayani, W.: Adomian decomposition method with green’s function for sixth-order boundary value problems. Comput. Math. Appl. 61(6), 1567–1575 (2011) CrossRefMATHMathSciNet
34.
35.
36.
37.
38.
Duan, J., Rach, R., Wazwaz, A.M., Chaolu, T., Wang, Z.: A new modified Adomian decomposition method and its multistage form for solving nonlinear boundary value problems with robin boundary conditions. Appl. Math. Model. (2013). doi:10.​1016/​j.​apm.​2013.​02.​002
39.
Abbaoui, K., Cherruault, Y.: Convergence of Adomian’s method applied to differential equations. Comput. Math. Appl. 28(5), 103–109 (1994) CrossRefMATHMathSciNet
40.
41.
Cherruault, Y., Adomian, G.: Decomposition methods: a new proof of convergence. Math. Comput. Model. 18(12), 103–106 (1993) CrossRefMATHMathSciNet
42.
Hosseini, M., Nasabzadeh, H.: On the convergence of Adomian decomposition method. Appl. Math. Comput. 182(1), 536–543 (2006) CrossRefMATHMathSciNet
Metadaten
Titel
The Adomian decomposition method with Green’s function for solving nonlinear singular boundary value problems
verfasst von
Randhir Singh
Jitendra Kumar
Publikationsdatum
01.02.2014
Verlag
Springer Berlin Heidelberg
Erschienen in
Journal of Applied Mathematics and Computing / Ausgabe 1-2/2014
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI
https://doi.org/10.1007/s12190-013-0699-4

Weitere Artikel der Ausgabe 1-2/2014

Journal of Applied Mathematics and Computing 1-2/2014 Zur Ausgabe

Original Research

Preconditioning analysis of the one dimensional incremental unknowns method on nonuniform meshes

Original Research

Existence of homoclinic solutions for second order Hamiltonian systems with general potentials

Original Research

Optimal control for an age-dependent predator-prey system in a polluted environment

Original Research

A global convergent quasi-Newton method for systems of monotone equations

Original Research

Positive solutions for nonlinear Caputo fractional differential equations with integral boundary conditions

Original Research

Existence of solutions for nonlinear high-order fractional boundary value problem with integral boundary condition

Premium Partner

    Bildnachweise