A comparison of Adomian decomposition method and RK4 algorithm on Volterra integro differential equations of 2nd kind
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2015-09-21 https://doi.org/10.14419/ijamr.v4i4.4965
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Volterra Integro differential equations, Adomian decomposition method, Adomian polynomial, Runge-Kutta4, Absolute error. -
Abstract
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. -
References
[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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How to Cite
M.C, K., M.Y, S., & S.P, M. (2015). A comparison of Adomian decomposition method and RK4 algorithm on Volterra integro differential equations of 2nd kind. International Journal of Applied Mathematical Research, 4(4), 481-487. https://doi.org/10.14419/ijamr.v4i4.4965Received date: 2015-07-01
Accepted date: 2015-09-14
Published date: 2015-09-21