A comparison of Adomian decomposition method and RK4 algorithm on Volterra integro differential equations of 2nd kind


  • Kekana M.C Tshwane university of TechnologyPrivate Bag X680Pretoria001South Africa
  • Shatalov M.Y
  • Moshokoa S.P






Volterra Integro differential equations, Adomian decomposition method, Adomian polynomial, Runge-Kutta4, Absolute error.


In this paper, Volterra Integro differential equations are solved using the Adomian decomposition method. The solutions are obtained in form of infinite series and compared to Runge-Kutta4 algorithm. The technique is described and illustrated with examples; numerical results are also presented graphically. The software used in this study is mathematica10.


[1] G Adomian, Solving Frontier Problems of Physics, Kluwer, Boston, 1994.

[2] G Adomian , Nonlinear Stochastic operator Equations Frontier, Academic Press, San Diego, 1986.

[3] G Adomian, “A review of the decomposition method and some recent results for nonlinear equationâ€, Math.Comput.Modelling, No7, (1992), pp. 17-43.

[4] G Adomian, R.Rach, “Equality of partial solutions in the decomposition method for linear or nonlinear partial differential equationsâ€, Comput.Math.Appl, No.12, (1990), pp. 9-12.

[5] J.Y. Edwards, J.A. Roberts, N.J. Ford, “A comparison of Adomian’s decomposition method and Runge-Kutta methods for approximate solution of some predator-prey model equations â€, Manchester Centre of Computational Mathematics, (1997), pp. 1-17.

[6] S.L El_Sayed, M.R. Abdel-Aziz, “A comparison of Adomian’s decomposition method and wavelet-Galerkin method for integro differential equationsâ€, Appl.Math.Comput, No.136, (2003), pp. 151-159.

[7] R.Rach, “On the Adomian decomposition method and comparison with Picard’s methodâ€, J.Math.Appl, No 128 (1987), pp 480-483.

[8] A.M Wazwaz, “A new algorithm for calculating non-linear operatorâ€, Appl.Math.Comput, No.111, (2001), 32-51.

[9] Z.M. Odibat, “Differential transform method for solving Volterra integral equation with separate kernelâ€, Math.Comput. Modelling, No. 48, (2008), pp. 1144-1149.

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