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

Authors

  • Wafa Abdelkareem Hassan Abdelkareem Hassan Department of Mathematics, Faculty of Science, University of Benghazi, Libya Author

DOI:

https://doi.org/10.71147/d1hnt028

Keywords:

Nonlinear Fredholm-Volterra Integro-Differential Equations; Sumudu Transform method; Adomian Decomposition Method.

Abstract

 

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.

 

References

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.

Abdou. M. A., Salama. F. A(2004). Volterra-fredholm integral equation of the first kind and spectral relationships, Appl. Math. Comput. ( 153).

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.

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.

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.

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.

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.

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.

Fawzi.(2003)A. Mathematical Model of Adomian Polynomials, Appl. Math. Comput. 141, 447.

Hassan. E., Adem. K.., and Berian. F.(2010). A new integral transform and associated distributions, Integral Transforms and Special Functions, 21( 5), 367-379.

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.

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.

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.

Salıh Y.(2002).Taylor polynomial solutions of nonlinear volterra-fredholm integral equations, Appl. Matt. Comput. 127 , 195-206.

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.

Wazwaz, A.M. (2011) Linear and Nonlinear Integral Equations: Methods and Applications. Springer-Verlag, Beijing.

Downloads

Published

2025-03-14

Issue

Section

Original Articles

How to Cite

Solving Nonlinear Volterra-Fredholm Integro-Differential Equations of the Second Kind by Combining the Sumudu Transform and the Adomian Decomposition Method. (2025). Derna Academy Journal for Applied Sciences, 3(2), 161-172. https://doi.org/10.71147/d1hnt028

Similar Articles

You may also start an advanced similarity search for this article.