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http://dx.doi.org/10.12941/jksiam.2017.21.017

THE COMBINED MODIFIED LAPLACE WITH ADOMIAN DECOMPOSITION METHOD FOR SOLVING THE NONLINEAR VOLTERRA-FREDHOLM INTEGRO DIFFERENTIAL EQUATIONS  

HAMOUD, AHMED A. (RESEARCH SCHOLAR AT. DEPARTMENT OF MATHEMATICS, DR. BAM UNIVERSITY)
GHADLE, KIRTIWANT P. (DEPARTMENT OF MATHEMATICS, DR. BABASAHEB AMBEDKAR MARATHWADA UNIVERSITY)
Publication Information
Journal of the Korean Society for Industrial and Applied Mathematics / v.21, no.1, 2017 , pp. 17-28 More about this Journal
Abstract
A combined form of the modified Laplace Adomian decomposition method (LADM) is developed for the analytic treatment of the nonlinear Volterra-Fredholm integro differential equations. This method is effectively used to handle nonlinear integro differential equations of the first and the second kind. Finally, some examples will be examined to support the proposed analysis.
Keywords
Adomian decomposition method; Integro differential equation; Laplace transform;
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1 A.M. Wazwaz, Linear and nonlinear integral equations methods and applications, Springer, Heidelberg Dordrecht London New York, 2011.
2 A. M. Jerri, Introduction to integral equations with applications, New York, Wiley, 1999.
3 A. A. Hamoud and K. P. Ghadle, On the numerical solution of nonlinear Volterra-Fredholm integral equations by variational iteration method, International Journal of Advanced Scientific and Technical Research, 3 (2016), 45-51.
4 A.M. Wazwaz, The combined Laplace transform-Adomian decomposition method for handling nonlinear Volterra integro differential equations, Applied Mathematics and Computation, 216 (2010), 1304-1309.   DOI
5 A.M. Wazwaz, The modified decomposition method for analytic treatment of nonlinear integral equations and systems of nonlinear integral equations, International Journal of Computer Mathematics, 82(9) (2005), 1107-1115.   DOI
6 M. Ghasemi, M. Kajani and E. Babolian, Application of he's homotopy perturbation method to nonlinear integro differential equations, Applied Mathematics and Computation, 188 (2007), 538-548.   DOI
7 A. A. Khajehnasiri, Numerical solution of nonlinear 2D Volterra-Fredholm integro differential equations by two-dimensional triangular function, International Journal of Applied and Computational Mathematics, 2(4) (2015), 1-17.
8 F. S. Fadhel, A. O. Mezaal and S. H. Salih, Approximate solution of the linear mixed Volterra-Fredholm integro differential equations of second kind by using variational iteration method, Al-Mustansiriyah Journal of Science, 24(5) (2013), 137-146.
9 S. B. Shadan, The use of iterative method to solve two-dimensional nonlinear Volterra-Fredholm integrodifferential equations, Journal of Communication in Numerical Analysis, 2012 (2012), 1-20.
10 M. A. Araghi and S. S. Behzadi, Solving nonlinear Volterra-Fredholm integro-differential equations using the modified Adomian decomposition Method, Computational Methods in Applied Mathematics, 9 (2009), 1-11.
11 M. Hussain and M. Khan, Modified Laplace decomposition method, Applied Mathematical Sciences, 4 (2010), 1769-1783.
12 S. M. El-Sayed, D. Kaya and S. Zarea, The decomposition method applied to solve high-order linear Volterra-Fredholm integro differential equations, International Journal of Nonlinear Sciences and Numerical Simulation, 5(2) (2004), 105-112.   DOI
13 A. Abubakar and O. A. Taiwo, Integral collocation approximation methods for the numerical solution of high-orders linear Fredholm-Volterra integro-differential equations, American Journal of Computational and Applied Mathematics, 4(4) (2014), 111-117.
14 S. H. Behiry and S. I. Mohamed, Solving high-order nonlinear Volterra-Fredholm integro-differential equations by differential transform method, Natural Science, 4(8) (2012), 581-587.   DOI
15 H. R. Marzban and S. M. Hoseini, Solution of nonlinear Volterra-Fredholm integro differential equations via hybrid of Block-Pulse functions and lagrange interpolating polynomials, Advances in Numerical Analysis, 868(279) (2012), 1-14.
16 Y. Salih and S. Mehmet, The approximate solution of higher order linear Volterra-Fredholm integro differential equations in term of Taylor polynomials, Applied Mathematics and Computation, 112 (2000), 291-308.   DOI
17 J. Manafianheris, Solving the integro-differential equations using the modified Laplace Adomian decomposition method, Journal of Mathematical Extension, 6(1) (2012), 41-55.
18 E. Babolian, Z. Masouri and S. Hatamzadeh, New direct method to solve nonlinear Volterra-Fredholm integral and integro differential equation using operational matrix with Block-Pulse functions, Progress in Electromagnetics Research B, 8 (2008), 59-76.   DOI
19 N. S. Elgazery, Numerical solution for the Falkner-Skan equation, Chaos, Solitons and Fractals, 35 (2008), 738-746.   DOI