Korean J. Math. Vol. 25 No. 3 (2017) pp.323-334
DOI: https://doi.org/10.11568/kjm.2017.25.3.323

The reliable modified of Laplace adomian decomposition method to solve nonlinear interval Volterra-Fredholm integral equations

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Ahmed Hamoud
Kirtiwant Ghadle


In this paper, we propose a combined form for solving nonlinear interval Volterra-Fredholm integral equations of the second kind based on the modifying Laplace Adomian decomposition method. We find the exact solutions of nonlinear interval Volterra-Fredholm integral equations with less computation as compared with standard decomposition method. Finally, an illustrative example has been solved to show the efficiency of the proposed method.

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[1] S.C. Akan and U.C. Akan, On Solvability of Some Nonlinear Fractional Interval Integral Equations, Fractional Differential Calculus, 7 2 (2017), 235-246. Google Scholar

[2] A.M. Jerri, Introduction to Integral Equations with Applications, New York, Wiley, 1999. Google Scholar

[3] A. Hamoud and K. Ghadle, On the Numerical Solution of Nonlinear VolterraFredholm Integral Equations by Variational Iteration Method, International Journal of Advanced Scientific and Technical Research, 3 (2016), 45-51. Google Scholar

[4] A. Hamoud and K. Ghadle, The Combined Modified Laplace with Adomian Decomposition Method for Solving the Nonlinear Volterra-Fredholm Integro Differential Equations, J. Ksiam, 21 1 (2017), 17-28. Google Scholar

[5] M. Hussain and M. Khan, Modified Laplace Decomposition Method, Applied Mathematical Sciences, 4 36 (2010), 1769-1783. Google Scholar

[6] M. Hussain and M. Khan, Application of Laplace Decomposition Method on Semi-Infinite Domain, Numer Algor, Springer Science+Business Media. 56 (2011), 211-218. Google Scholar

[7] S. Salahshour and M. Khan, Exact Solutions of Nonlinear Interval Volterra Integral Equations, Int. J. Industrial Mathematics, 4 4 (2012), 375-388. Google Scholar

[8] T. Vinh An, N. Dinh Phu and N. Van Hoa, A Note on Solutions of IntervalValued Volterra Integral Equations, Journal of Integral Equations And Applications, 26 1 (2014), 1-14. Google Scholar

[9] 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. Google Scholar

[10] A.M. Wazwaz, Linear and Nonlinear Integral Equations Methods and Applications, Springer, Heidelberg Dordrecht London New York, 2011. Google Scholar