nach oben

Neural Computing and Applications

Erschienen in:

01.04.2016 | Original Article

Difference kernel iterative method for linear and nonlinear partial differential equations

verfasst von: Yasir Khan, Naeem Faraz, Zdenek Smarda

Erschienen in: Neural Computing and Applications | Ausgabe 3/2016

Einloggen

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

search-config

KI-gestützte Suche

Aus

Abstract

The purpose of this paper was to propose a new method to solve partial differential equations arising in the field of science and engineering. In this new method, we have reduced the multiple integrals into a single integral and expressed it in terms of a difference kernel. To make the calculation easy and convenient, we have used the Laplace transformation to solve the difference kernel. The method is very simple, easy to understand and calculation minimizing as compared to the Adomian decomposition method and the variational iteration method. Some examples are given to verify the reliability and efficiency of the method.

Vorheriger Artikel Feature-level fusion of mental task’s brain signal for an efficient identification system

Nächster Artikel Construction of S-box based on chaotic Boolean functions and its application in image encryption

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

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

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

Khan Y, Austin F (2010) Application of the Laplace decomposition method to nonlinear homogeneous and non-homogenous advection equations. Z Naturforsch A 65a:849–853

Khan Y, Madani M, Yildirim A, Abdou MA, Faraz N (2011) A new approach to Van der Pol’s oscillator problem. Z Naturforsch A 66a:620–624

Khan Y, Vázquez-Leal H, Faraz N (2012) An efficient new iterative method for oscillator differential equation. Scientia Iranica 19:1473–1477CrossRef

Turkyilmazoglu M (2011) An optimal analytic approximate solution for the limit cycle of Duffing–van der Pol equation. J Appl Mech Trans ASME 78:021005CrossRef

Turkyilmazoglu M (2011) An optimal variational iteration method. Appl Math Lett 24:762–765MathSciNetCrossRefMATH

Khan Y, Vázquez-Leal H, Faraz N (2013) An efficient iterated method for mathematical biology model. Neural Comput Appl 23:677–682CrossRef

Gadkar KG, Gunawan R, Doyle FJ (2005) Iterative approach to model identification of biological networks. BMC Bioinform 6:155–175CrossRef

Sweilam NH, Khader MM, Al-Bar RF (2008) Nonlinear focusing Manakov systems by variational iteration method and Adomian decomposition method. J Phys Conf Ser 96:012164CrossRef

Khan Y (2014) Two-dimensional boundary layer flow of chemical reaction MHD fluid over a shrinking sheet with suction and injection. J Aerosp Eng 27:04014019CrossRef

10.

Yildirim A, Askari H, Saadatnia Z, Kalami Yazdi M, Khan Y (2011) Analysis of nonlinear oscillations of a punctual charge in the electric field of a charged ring via a Hamiltonian approach and the energy balance method. Comput Math Appl 62:486–490MathSciNetCrossRefMATH

11.

Khan Y, Akbarzade M (2012) Dynamic analysis of non-linear oscillator equation arising in double-sided driven clamped microbeam-based electromechanical resonator. Z Naturforsch A 67a:435–440

12.

He JH, Wan YQ, Guo Q (2004) An iteration formulation for normalized diode characteristics. Int J Circuit Theory Appl 32:629–632CrossRefMATH

13.

Yang F, Fonder GA (1996) An iterative solution method for dynamic response of bridge–vechicles systems. Earthq Eng Struct Dyn 25:195–215CrossRef

14.

Omid BN, Wriggers P (1986) A two-level iteration method for solution of contact problems. Comput Methods Appl Mech Eng 54:131–144MathSciNetCrossRefMATH

15.

Hribersek M, Skerget L (1996) Iterative methods in solving Navier–Stokes equations by the boundary element method. Int J Numer Methods Eng 39:115–139CrossRefMATH

16.

Khan Y, Faraz N, Yildirim A, Wu Q (2011) A series solution of the long porous slider. Tribol Trans 54:187–191CrossRef

17.

Khan Y, Wu Q, Faraz N, Yildirim A (2011) The effects of variable viscosity and thermal conductivity on a thin film flow over a shrinking/stretching sheet. Comput Math Appl 61(11):3391–3399MathSciNetCrossRefMATH

18.

Hetmaniok E, Nowak I, Slota D, Wituła R (2012) Application of the homotopy perturbation method for the solution of inverse heat conduction problem. Int Commun Heat Mass Transf 39:30–35CrossRef

19.

He JH (1999) Variational iteration method, a kind of non-linear analytical technique, some examples. Int J Nonlinear Mech 34:699–708CrossRefMATH

20.

Wazwaz AM (2010) The combined Laplace transform–Adomian decomposition method for handling nonlinear Volterra integro–differential equations. Appl Math Comput 216:1304–1309MathSciNetMATH

21.

Thongmoon M, Pusjuso S (2010) The numerical solutions of differential transform method and the Laplace transform method for a system of differential equations. Nonlinear Anal Hybrid Syst. 4:425–431MathSciNetCrossRefMATH

22.

Abassy TA, EI-Tawil MA, EI-Zoheiry H (2007) Exact solutions of some nonlinear partial differential equations using the variational iteration method linked with Laplace transforms and the Pade technique. Comput Math Appl 54:940–954MathSciNetCrossRefMATH

23.

Khan Y, Wu Q (2011) Homotopy Perturbation transform method for nonlinear equations using He’s polynomials. Comput Math Appl 61:1963–1967MathSciNetCrossRefMATH

24.

Khan Y, Vázquez-Leal H, Faraz N (2013) An auxiliary parameter method using Adomian polynomials and Laplace transformation for nonlinear differential equations. Appl Math Model 37:2702–2708MathSciNetCrossRef

25.

Khan Y (2009) An effective modification of the laplace decomposition method for nonlinear equations. Int J Nonlinear Sci Numer Simul 10:1373–1376

26.

Vajravelu K, Rollins D (2004) Hydromagnetic flow of a second grade fluid over a stretching sheet. Appl Math Comput 148:783–791MathSciNetMATH

27.

Faraz N, Khan Y, Austin F (2010) An alternative approach to differential-difference equation by using variational iteration algorithm. Z Naturforsch 65a:1055–1059

Titel: Difference kernel iterative method for linear and nonlinear partial differential equations
verfasst von: Yasir Khan
Naeem Faraz
Zdenek Smarda
Publikationsdatum: 01.04.2016
Verlag: Springer London
Erschienen in: Neural Computing and Applications / Ausgabe 3/2016
Print ISSN: 0941-0643
Elektronische ISSN: 1433-3058
DOI: https://doi.org/10.1007/s00521-015-1886-z

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

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

Springer Professional "Wirtschaft"

Springer Professional "Technik"

Springer Professional "Wirtschaft+Technik"

Weitere Artikel der Ausgabe 3/2016

Transferred IR pedestrian detector toward distinct scenarios adaptation

Using neural networks to integrate structural analysis package and optimization package

An integrated model for green supplier selection under fuzzy environment: application of data envelopment analysis and genetic programming approach

A hybrid data mining model in analyzing corporate social responsibility

A novel integral extension LMD method based on integral local waveform matching

Analysis and forecasting of IPO underpricing

Premium Partner