THE RELIABLE MODIFIED OF ADOMIAN DECOMPOSITION METHOD FOR SOLVING INTEGRO-DIFFERENTIAL EQUATIONS

다국어 초록 (Multilingual Abstract)

In this article, we discussed semi-analytical approximated methods for solving mixed Volterra-Fredholm integro-differential equations, namely: Adomian decomposition method and modified Adomian decomposition method. Moreover, we prove the unique-ness results and convergence of the techniques. Finally, an example is included to demonstrate the validity and applicability of the proposed techniques.

목차 (Table of Contents)

• 1. Introduction 2. Nonlinear Mixed Volterra-Fredholm Integro-Differential Equation of Second Kind 3. Description of the Methods 4. Uniqueness and Convergence Results 5. Numerical Example 6. Conclusion

참고문헌 (Reference)

1 J.H. He, "Variational iteration method for solving integro-differential equations" 367 : 188-191, 2007

2 A.A. Hamoud, "Usage of the modi-fied variational iteration technique for solving Fredholm integro-differential equa-tions" 9 (9): 895-902, 2019

3 A.A. Hamoud, "Usage of the homotopy analysis method for solving fractional Volterra-Fredholm integro-differential equation of the second kind" 49 (49): 301-315, 2018

4 S.B. Shadan, "The use of iterative method to solve two-dimensional nonlinear Volterra-Fredholm integro-differential equations" 1-20, 2012

5 Ahmed A. Hamoud, "The reliable modified of Laplace adomian decomposition method to solve nonlinear interval Volterra-Fredholm integral equations" 강원경기수학회 25 (25): 323-334, 2017

6 A.A. Hamoud, "The reliable modified Laplace Adomian decomposition method to solve fractional Volterra-Fredholm integro-differential equations" 26 : 171-184, 2019

7 S.M. El-Sayed, "The decomposition method applied to solve high-order linear Volterra-Fredholm integro-differential equations" 5 (5): 105-112, 2004

8 A.M. Wazwaz, "The combined Laplace transform-Adomian decomposition method for handling nonlinear Volterra integro-differential equations" 216 : 1304-1309, 2010

9 A.A. Hamoud, "The approximate solutions of fractional integro-differential equations by using modified Adomian decomposition method" 5 (5): 21-39, 2019

10 A.A. Hamoud, "The approximate solutions of fractional Volterra-Fredholm integro-differential equations by using analytical techniques" 7(25) (7(25)): 41-58, 2018

11 Y. Salih, "The approximate solution of higher order linear Volterra-Fredholm integro-differential equations in term of Taylor polynomials" 112 : 291-308, 2000

12 A.A. Hamoud, "Some new existence, uniqueness and convergence results for fractional Volterra-Fredholm integro-differential equations" 5 (5): 58-69, 2019

13 J. Manafianheris, "Solving the integro-differential equations using the modified Laplace Adomian decomposition method" 6 (6): 41-55, 2012

14 M.A. Araghi, "Solving nonlinear Volterra-Fredholm integro-differential equations using the modified Adomian decomposition method" 9 : 321-331, 2009

15 A.A. Hamoud, "Solving integro-differential equations by using numerical techniques" 14 (14): 3219-3225, 2019

16 S.H. Behiry, "Solving high-order nonlinear Volterra-Fredholm integro-differential equations by differential transform method" 4 (4): 581-587, 2012

17 H.R. Marzban, "Solution of nonlinear Volterra-Fredholm integro-differential equations via hybrid of Block-Pulse functions and Lagrange interpo-lating polynomials" Hindawi Publishing Corporation 868 (868): 1-14, 2012

18 E. Babolian, "New direct method to solve nonlin-ear Volterra-Fredholm integral and integro differential equation using operational matrix with Block-Pulse functions" 8 : 59-76, 2008

19 A.A. Hamoud, "Modified Laplace decomposition method for frac-tional Volterra-Fredholm integro-differential equations" 6 (6): 91-104, 2018

20 A.A. Hamoud, "Modified Adomian decomposition method for solving fuzzy Volterra-Fredholm integral equations" 85 (85): 52-69, 2018

21 A.M. Wazwaz, "Linear and Nonlinear Integral Equations Methods and Applica-tions" Springer 2011

22 A.M. Jerri, "Introduction to Integral Equations with Applications" Wi-ley 1999

23 A.A. Hamoud, "Homotopy analysis method for the first order fuzzy Volterra-Fredholm integro-differential equations" 11 (11): 857-867, 2018

24 A.A. Hamoud, "Existence and uniqueness results for nonlinear Volterra-Fredholm integro-differential equations" 23 (23): 797-805, 2018

25 A.A. Hamoud, "Existence and uniqueness of the solution for Volterra-Fredholm integro-differential equations" 11 (11): 692-701, 2018

26 A.A. Hamoud, "Existence and uniqueness of solutions for frac-tional mixed Volterra-Fredholm integro-differential equations" 60 (60): 375-395, 2018

27 A.A. Hamoud, "Existence and unique-ness theorems for fractional Volterra-Fredholm integro-differential equations" 31 (31): 333-348, 2018

28 A.A. Hamoud, "Existence and convergence results for caputo fractional Volterra integro-differential equations" 41 : 109-122, 2018

29 F.S. Fadhel, "Approximate solution of the linear mixed Volterra-Fredholm integro-differential equations of second kind by using variational iteration method" 24 (24): 137-146, 2013

30 M. Ghasemi, "Application of He's homotopy pertur-bation method to nonlinear integro differential equations" 188 : 538-548, 2007

31 A.A. Hamoud, "A study of some iterative methods for solving fuzzy Volterra-Fredholm integral equations" 11 (11): 1228-1235, 2018

32 A.M. Wazwaz, "A reliable modification of Adomian decomposition method" 102 : 77-86, 1999