Numerical Solution of Nonlinear Volterra Integro-Differential Equations of Fractional Order by Using Adomian Decomposition Method

Abstract:

In this work we present a computational method for for solving a class of nonlinear Volterra integro-differential equations of fractional order which is based on Adomian Decom-position Method. Convergence analysis is dependable enough to estimate the maximum absolute truncated error of the Adomian series solution. Numerical example is included to demonstrate the validity and applicability of the method.

• Periodical: Applied Mechanics and Materials (Volumes 635-637)
• Pages: 1582-1585
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.635-637.1582
• Online since: September 2014
• Authors: Li Feng Wang, Yun Peng Ma*, Yong Qiang Yang
• Keywords: Adomian Method, Convergence Analysis, Error Estimate, Nonlinear Volterra Integro-Differential Equations, Numerical Solution

References

[1] G. Adomian: Stochastic System (Academic Press, 1983).

[2] G. Adomian: Nonlinear Stochastic Operator Equations (Academic Press, San Diego 1986).

[3] M. EI-Tawil, M. Saleh: Int. J. Differ. Equ. Appl. Vol. 6 (2002), pp.411-422.

[4] I.L. EI-Kalla: Commun. Nonlinear Sci. Numer. Simul. Vol. 16 (2011), p.1408–1413.

[5] J.H. He: Bull Sci Technol Vol. 15 (1999), p.86–90.

[6] M. ur Rehman: Commun. Nonlinear Sci. Numer. Simulat. Vol. 16 (2011), p.4163–4173.

[7] P.Y. Qin, X.D. Zhang: Mathematic Numerica Sinica (in Chinese) Vol. 30 (2008), pp.305-310.

[8] I.L. EI-Kalla: Appl. Math. Lett. Vol. 21 (2008), pp.372-376.

[9] I.L. EI-Kalla: Int. J. Differ. Equ. Appl. Vol. 10 (2005), pp.225-234.