%0 Journal Article %T Laplace discrete decomposition method for solving nonlinear Volterra-Fredholm integro-differential equations %A Dawood, Lafta A. %A Hamoud, Ahmed A. %A Mohammed, Nedal M. %J Journal of Mathematics and Computer Science %D 2020 %V 21 %N 2 %@ ISSN 2008-949X %F Dawood2020 %X In this article, a new modification of the Adomian Decomposition Method (ADM) that is called the Laplace Discrete Adomian Decomposition Method (LDADM) is applied to non-homogeneous nonlinear Volterra-Fredholm integro-differential equations. This method is based upon the Laplace Adomian decomposition method coupled with some quadrature rules of numerical integration. The performance of the proposed method is verified through absolute error measures between the approximated solutions and exact solutions. The series of experimental numerical results show that our proposed method performs in high accuracy and efficiency. The study highlights that the proposed method could be used to overcome the analytical approaches in solving nonlinear Volterra-Fredholm integro-differential equations. %9 journal article %R 10.22436/jmcs.021.02.07 %U http://dx.doi.org/10.22436/jmcs.021.02.07 %P 158--163 %0 Journal Article %T Numerical algorithm for solving two-point, second-order periodic boundary value problems for mixed integro-differential equations %A O. Abu Arqub %A M. Al-Smadi %J Appl. Math. Comput. %D 2014 %V 243 %F Arqub2014 %0 Journal Article %T Solving Fredholm integro-differential equations using reproducing kernel Hilbert space method %A O. Abu Arqub %A M. Al-Smadi %A N. Shawagfeh %J Appl. Math. Comput. %D 2013 %V 219 %F Arqub2013 %0 Journal Article %T Solutions of Bagley--Torvik and Painleve equations of fractional order using iterative reproducing kernel algorithm %A O. Abu Arqub %A B. Maayah %J Neural Comput. Appl. %D 2018 %V 29 %F Arqub2018 %0 Journal Article %T A Chebyshev collocation method for the solution of linear integro-differential equations %A A. Akyüz %A M. Sezer %J Int. J. Comput. Math. %D 1999 %V 72 %F Akyüz1999 %0 Journal Article %T Approximate solutions of Volterra-Fredholm integro-differential equations of fractional order %A S. Alkan %A V. F. Hatipoglu %J Tbilisi Math. J. %D 2017 %V 10 %F Alkan2017 %0 Journal Article %T Some modifications of adomian decomposition methods for nonlinear partial differential equations %A M. Al-Mazmumy %A H. Al-Malki %J Int. J. Res. Agricul. Sci. %D 2015 %V 23 %F Al-Mazmumy2015 %0 Journal Article %T An efficient modification of the Adomian decomposition method for solving integro-differential equations %A H. O. Bakodah %A M. Al-Mazmumy %A S. O. Almuhalbedi %J Math. Sci. Lett. %D 2017 %V 6 %F Bakodah2017 %0 Book %T Computational Methods for Integral Equations %A L. M. Delves %A J. L. Mohamed %D 1985 %I Cambridge University Press %C Cambridge %F Delves1985 %0 Journal Article %T Continuous Runge-Kutta methods for neutral Volterra integro-differential equations with delay %A W. H. Enright %A M. Hu %J Appl. Numer. Math. %D 1997 %V 24 %F Enright1997 %0 Journal Article %T Existence and uniqueness results for nonlinear Volterra-Fredholm integro differential equations %A A. A. Hamoud %A M. S. Bani Issa %A K. P. Ghadle %J Nonlinear Funct. Anal. Appl. %D 2018 %V 23 %F Hamoud2018 %0 Journal Article %T Usage of the modified variational iteration technique for solving Fredholm integro-differential equations %A A. A. Hamoud %A L. A. Dawood %A K. P. Ghadle %A S. M. Atshan %J Int. J. Mech. Prod. Eng. Res. Develop. %D 2019 %V 9 %F Hamoud2019 %0 Journal Article %T The combined modified Laplace with Adomian decomposition method for solving the nonlinear Volterra-Fredholm integro-differential equations %A A. A. Hamoud %A K. P. Ghadle %J J. Korean Soc. Ind. Appl. Math. %D 2017 %V 21 %F Hamoud2017 %0 Journal Article %T The reliable modified of Laplace Adomian decomposition method to solve nonlinear interval Volterra-Fredholm integral equations %A A. A. Hamoud %A K. P. Ghadle %J Korean J. Math. %D 2017 %V 25 %F Hamoud2017 %0 Journal Article %T Existence and uniqueness of solutions for fractional mixed Volterra-Fredholm integro-differential equations %A A. A. Hamoud %A K. P. Ghadle %J Indian J. Math. %D 2018 %V 60 %F Hamoud2018 %0 Journal Article %T Homotopy analysis method for the first order fuzzy Volterra-Fredholm integro-differential equations %A A. A. Hamoud %A K. P. Ghadle %J Indonesian J. Ele. Eng. Comput. Sci. %D 2018 %V 11 %F Hamoud2018 %0 Journal Article %T Modified Adomian decomposition method for solving fuzzy Volterra-Fredholm integral equations %A A. A. Hamoud %A K. P. Ghadle %J J. Indian Math. Soc. %D 2018 %V 85 %F Hamoud2018 %0 Journal Article %T Modified Laplace decomposition method for fractional Volterra-Fredholm integro-differential equations %A A. A. Hamoud %A K. P. Ghadle %J J. Math. Model. %D 2018 %V 6 %F Hamoud2018 %0 Journal Article %T The approximate solutions of fractional Volterra-Fredholm integro-differential equations by using analytical techniques %A A. A. Hamoud %A K. P. Ghadle %J Probl. Anal. Issues Anal. %D 2018 %V 7 %F Hamoud2018 %0 Journal Article %T Usage of the homotopy analysis method for solving fractional Volterra-Fredholm integro-differential equation of the second kind %A A. A. Hamoud %A K. P. Ghadle %J Tamkang J. Math. %D 2018 %V 49 %F Hamoud2018 %0 Journal Article %T Some new existence, uniqueness and convergence results for fractional Volterra-Fredholm integro-differential equations %A A. A. Hamoud %A K. P. Ghadle %J J. Appl. Comput. Mech. %D 2019 %V 5 %F Hamoud2019 %0 Journal Article %T The approximate solutions of fractional integro-differential equations by using modified Adomian decomposition method %A A. A. Hamoud %A K. P. Ghadle %A S. M. Atshan %J Khayyam J. Math. %D 2019 %V 5 %F Hamoud2019 %0 Journal Article %T Existence and uniqueness theorems for fractional Volterra-Fredholm integro-differential equations %A A. A. Hamoud %A K. P. Ghadle %A M. S. Bani Issa %A Giniswamy %J Int. J. Appl. Math. %D 2018 %V 31 %F Hamoud2018 %0 Journal Article %T An existence and convergence results for Caputo fractional Volterra integro-differential equations %A A. A. Hamoud %A K. P. Ghadle %A P. A. Pathade %J Jordan J. Math. Stat. %D 2019 %V 12 %F Hamoud2019 %0 Journal Article %T The reliable modified Laplace Adomian decomposition method to solve fractional Volterra-Fredholm integro-differential equations %A A. A. Hamoud %A K. H. Hussain %A K. P. Ghadle %J Dyn. Contin. Discrete Impuls. Syst. Ser. B Appl. Algorithms %D 2019 %V 26 %F Hamoud2019 %0 Journal Article %T Solving Fredholm integro-differential equations by using numerical techniques %A A. A. Hamoud %A K. H. Hussain %A N. M. Mohammed %A K. P. Ghadle %J Nonlinear Funct. Anal. Appl. %D 2019 %V 24 %F Hamoud2019 %0 Journal Article %T A study of some effective techniques for solving Volterra-Fredholm integral equations %A A. A. Hamoud %A N. M. Mohammed %A K. P. Ghadle %J Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. %D 2019 %V 26 %F Hamoud2019 %0 Journal Article %T Some new uniqueness results for fractional integro-differential equations %A K. H. Hussain %A A. A. Hamoud %A N. M. Mohammed %J Nonlinear Funct. Anal. Appl. %D 2019 %V 24 %F Hussain2019 %0 Journal Article %T A Taylor collocation method for the solution of linear integro-differential equations %A A. Karamete %A M. Sezer %J Int. J. Comput. Math. %D 2002 %V 79 %F Karamete2002 %0 Journal Article %T A Laplace decomposition algorithm applied to a class of nonlinear differential equations %A S. A. Khuri %J J. Appl. Math. %D 2001 %V 1 %F Khuri2001 %0 Journal Article %T An Algorithm for solving initial value problems using Laplace Adomian decomposition method %A O. Kiymaz %J Appl. Math. Sci. (Ruse) %D 2009 %V 3 %F Kiymaz2009 %0 Journal Article %T Solving linear integro-differential equations system by using rationalized Haar functions method %A K. Maleknejad %A F. Mirzaee %A S. Abbasbandy %J Appl. Math. Comput. %D 2004 %V 155 %F Maleknejad2004 %0 Journal Article %T Solving linear integro-differential equation system by Galerkin methods with hybrid functions %A K. Maleknejad %A M. Tavassoli Kajani %J Appl. Math. Comput. %D 2004 %V 159 %F Maleknejad2004 %0 Journal Article %T Application of the fractional differential transform method to fractional-order integro-differential equations with nonlocal boundary conditions %A D. Nazari %A S. Shahmorad %J J. Comput. Appl. Math. %D 2010 %V 234 %F Nazari2010 %0 Book %T Linear and Nonlinear Integral Equations Methods and Applications %A A.-M. Wazwaz %D 2011 %I Springer %C Heidelberg %F Wazwaz2011