Solving Nonlinear Volterra-Fredholm Integro-Differential Equations of the Second Kind by Combining the Sumudu Transform and the Adomian Decomposition Method

• Wafa Abdelkareem Hassan Abdelkareem Hassan

  Department of Mathematics, Faculty of Science, University of Benghazi, Libya

  Author

Aabstract

In this paper, we modify the Sumudu decomposition method, the Sumudu Adomian Decomposition Method (SADM) which is a combination of  the Sumudu transform method with the modified Adomian method and apply this method to solve mixed Fredholm-Volterra integro-differential equations, To study the performance of this technique, we introduced tow Numerical Examples of nonlinear Fredholm-Volterra  integro-differential equations , The result shows that the proposed method is simple, fast and easy to implement.

Abdou. M. A.(2003). On asymptotic methods for fredholm-volterra integral equation of the second kind in contact problems. J. Comp. Appl. Math. 154 , 431-446. DOI: https://doi.org/10.1016/S0377-0427(02)00862-2

Abdou. M. A., Salama. F. A(2004). Volterra-fredholm integral equation of the first kind and spectral relationships, Appl. Math. Comput. ( 153). DOI: https://doi.org/10.1016/S0096-3003(03)00619-2

Abdul-Majid, W.(2006). The modified decomposition method and Pade approximants for a boundary layer equation in unbounded domain, Applied Mathematics and Computation, vol. 177, ( 2), 737-744. DOI: https://doi.org/10.1016/j.amc.2005.09.102

Ahmed A.(2017), the combined modified laplace with Adomiandecomposition method for solving the nonlinear volterra-Fredholm differential equations, J. Ksiam , 21 ( 1), 17-28.

Ahmed. A., Kirtiwant. P.( 2017). The combined Modified Laplace with Adomian decomposition method for solving the nonlinear Volterra-Fredholm Integro Differential Equations, vol, 21, , (1), 17-28.

Ahmad,M. Ahmad, M and A, S, Mohamed.(2015)Sumudu decomposition method for solving fractional-order Logistic differential equation, Journal of advances in athematics 7(10):3632-2639 .

Ayyubi A. (2021). Numerical Solution of mixed linear volterra-fredholm integral equations by modified block pulse functions, Jurnal Riset dan Aplikasi Matematika (JRAM) 5(1), 1-9. DOI: https://doi.org/10.26740/jram.v5n1.p1-9

Abdul-Majid, W.,(1997) Necessary conditions for the appearance of noise terms in decomposition solution series, Applied Mathematics and Computation, 81( 2-3). 265-274. DOI: https://doi.org/10.1016/S0096-3003(95)00327-4

Dalal, A and Eman, A.March.(2002). Modified Decomposition Method For solving Fredholm Integro-Differential Equation using maple, International Journal of GEOMATE, 18(67) 84-89.

[10] Ebrahim, A., Mousa F, . Kurosh S., and Hamidreza E.(2009). Solution of the Falkner-Skan equation for wedge by Adomian Decomposition Method, Communications in Nonlinear Science and Numerical Simulation,14(. 3),724-733. DOI: https://doi.org/10.1016/j.cnsns.2007.11.002

Esmail B, Alireza, V, and Zahra, A.(2012).A Comparison Between Adomian’s Decomposition Method and the Homotopy Perturbation Method for Solving Nonlinear Differential Equations 12(8):793. DOI: https://doi.org/10.3923/jas.2012.793.797

Fariborzi, M., and Sadigh, Sh.(2009). Solving Nonlinear Volterra – Fredholm Integro-Differential Equations Using The Modified Adomian Decomposition Method, Computational Methods In Applied Mathematics , .9(.4).321-331. DOI: https://doi.org/10.2478/cmam-2009-0020

Fawzi.(2003)A. Mathematical Model of Adomian Polynomials, Appl. Math. Comput. 141, 447. DOI: https://doi.org/10.1016/S0096-3003(02)00266-7

Hassan. E., Adem. K.., and Berian. F.(2010). A new integral transform and associated distributions, Integral Transforms and Special Functions, 21( 5), 367-379. DOI: https://doi.org/10.1080/10652460903335061

Hassan E, Adem, K., and Said M. (2018). Application of Sumudu Decomposition Method to Solve Nonlinear System Fredholm and Volterra Integro differential Equations, International Journal of Applied Engineering Research,13(11), 9588-9595.

Hassan. I ., Francis.A., Gabriel. T.(2016). On the Solution of Volterra-Fredholm and Mixed Volterra-Fredholm Integral Equations Using the New Iterative Method Applied Mathematics, , 6(1), 1-5.

Hradyesh K.(2015).Numerical Simulation of Time-fractional Fourth Order Differential Equations via Homotopy Analysis Fractional Sumudu Transform Method, American Journal of Numerical Analysis, 3 ( 3), 2015, 52-64 .

Maleknejad. K., Hadizadeh. M.(1999). A new computational method for volterra- fredholm integral equations, Computer and Mathematics with Applications. 37 (9): 1-8. DOI: https://doi.org/10.1016/S0898-1221(99)00107-8

Mohsen, R, Yadollah O.(2005). Solution of Nonlinear Volterra-Hammerstein Integral Equations Via Rationalized Haar Functions, January 2001 Mathematical Problems in Engineering 180(2) 1-12. DOI: https://doi.org/10.1016/j.amc.2005.12.034

Rezvan , G. Jafar- saberi.n, and Mortaza, G.(2018). An Analytical and Approximate Solution for Nonlinear Volterra Partial Integro-Differential Equations with a Weakly Singular Kernel Using the Fractional Differential Transform Method,, April 2018, International Journal of Differential Equations8 (1)1-10. DOI: https://doi.org/10.1155/2018/7237680

Salıh Y.(2002).Taylor polynomial solutions of nonlinear volterra-fredholm integral equations, Appl. Matt. Comput. 127 , 195-206. DOI: https://doi.org/10.1016/S0096-3003(00)00165-X

Tavassoli, M Kajani, M. Ghasemi, and Esmail, B.(2007).solution of the nonlinear volterra-fredholm integral equations by using homotopy perturbation method. Appl. Matt. Comput, 188 , 446-449. DOI: https://doi.org/10.1016/j.amc.2006.10.015

Wazwaz, A.M. (2011) Linear and Nonlinear Integral Equations: Methods and Applications. Springer-Verlag, Beijing. DOI: https://doi.org/10.1007/978-3-642-21449-3

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