Analytical Approximations for Nonlinear Integro-Differential Equations

nabaa najdi hasan, Majid R. Nasif

Abstract


In this work, we are concerned with how to find a solution for the nonlinear integral
andointegro-differentialeequationsuusingttwoomethodsoLaplaceotransformiseries
idecomposition method (LTSDM) and Sumuduutransform series decomposition method
(STSDM). In these methods, the nonlinear part of the equation described in Adomian
idecomposition series. The Laplace and Sumudu methods are found to be reliable and
accurate. Four examples are discussed to check the applicability and the simplicity of these
methods. Finally, the results are tabulated and displayed graphically to make comparisons
between the approximate and exact solutions.

Keywords


Nonlinear Intgro-Differential Equation of Second Kind, Adomian Decomposition Method, Laplace Transform, Sumudu Transform.

Full Text:

PDF

References


Ilias S. Kotsireas , "A Survey on Solution Methods for Integral Equations" , June , 2008.

Fethi B. Muhammad and Ahmed A. Karaballi , "Sumudu transform fundamental properties investigations and applications" , Journal of Applied Mathematics and Stochastic Analysis , Volume 2006, Article ID 91083, p.p 1-23,May , 2006.

[Crossref]

Fethi B. Muhammad and Ahmed A. Karaballi , "Analytical Investigations of the Sumudu transform and Applications to integral Production Equayions ", Hindawi Publishing Corporation ,p.p 103-118 , Oct 2002.

[Crossref]

E.I. Akinola and I.A. Olopade , "Sumudu Transform Series Decomposition Method for Solving Nonlinear Volterra Integro-Differential Equations", International Journal of Innovation and Applied Studies ,Vol. 18 , No. 1 , , pp. 262-267 , Oct. 2016.

Ahmed A Hamoud and Dr.Kirtiwant P Ghadle , "The combined Modified Laplace with Adomian decomposition method for Solving the nonlinear Volterra-Fredholm Integro Differential Equations", J. KSIAM , Vol.21, No.1, p.p 17-28, March 2017.

Dimple Rani and Vinod Mishra , "Modification of Laplace Adomian Decomposition Method for Solving Nonlinear Volterra Integral and Integro-differential Equations based on Newton Raphson Formula", European Journal of Pure and Applied Mathematics , Vol. 11, No. 1 , p.p202-214 , January 2018.

[Crossref]

M. Rahman , "Integral Equations and their Applications", printed in Great Britain by Athenaeum Press Ltd.,WIT Press 2007.

Abdul-Majid Wazwaz , "A First Course in integral equations",2015 by World Scientific Publishing Co. Pte. Ltd.

[Crossref]

Abdul-Majid Wazwaz , " Linear and Nonlinear Integral Equation ",Higher Education Press,Beijing and Springer-Verlag Berlin Heidelberg 2011.

S. Z. Rida and A. S. Abedl-Rady "A Domian Decomposition Sumudu Transform Method for Solving Fractional Nonlinear Equations" Mathematical Sciences Letters ,vol. 5, No. 1, p.p 39 - 48 , Jan. 2016.

[Crossref]




DOI: http://dx.doi.org/10.23851/mjs.v30i3.675

Refbacks

  • There are currently no refbacks.


Copyright (c) 2019 Al-Mustansiriyah Journal of Science

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.


Copyright (c) 2018 by Al-Mustansiriyah Journal of Science
ISSN: 1814-635X (Print), ISSN: 2521-3520 (online)