Solving nth-Order Integro-Differential Equations Using the Combined Laplace Transform-Adomian Decomposition Method

DOI: 10.4236/am.2013.46121   PDF   HTML     4,757 Downloads   7,673 Views   Citations

Abstract

In this paper, the Combined Laplace Transform-Adomian Decomposition Method is used to solve nth-order integro-differential equations. The results show that the method is very simple and effective.

Share and Cite:

W. Al-Hayani, "Solving nth-Order Integro-Differential Equations Using the Combined Laplace Transform-Adomian Decomposition Method," Applied Mathematics, Vol. 4 No. 6, 2013, pp. 882-886. doi: 10.4236/am.2013.46121.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] A. Golbabai and M. Javidi, “Application of He’s Homotopy Perturbation Method for nth-Order Integro-Differential Equations,” Applied Mathematics and Computation, Vol. 190, No. 2, 2007, pp. 1409-1416. doi:10.1016/j.amc.2007.02.018
[2] X. F. Shang and D. F. Han, “Application of the Variational Iteration Method for Solving nth-Order IntegroDifferential Equations,” Journal of Computational and Applied Mathematics, Vol. 234, No. 5, 2010, pp. 14421447. doi:10.1016/j.cam.2010.02.020
[3] A. M. Wazwaz, “The-Combined Laplace Transform-Adomian Decomposition Method for Handling Nonlinear Volterra-Integro Differential Equations,” Applied Mathematics and Computation, Vol. 216, No. 4, 2010, pp. 1304-1309. doi:10.1016/j.amc.2010.02.023
[4] G. Adomian, “Stochastic Systems,” Academic Press, New York, 1983.
[5] G. Adomian, “Nonlinear Stochastic Operator Equations,” Academic Press, New York, 1986.
[6] G. Adomian, “Nonlinear Stochastic Systems Theory and Applications to Physics,” Kluwer Academic Publishers, Dordrecht, 1989. doi:10.1007/978-94-009-2569-4
[7] G. Adomian, “Solving Frontier Problems of Physics: The Decomposition Method,” Kluwer Academic Publishers, Dordrecht, 1994.
[8] K. Abbaoui and Y. Cherruault, “Convergence of Adomian’s Method Applied to Differential Equations,” Mathematical and Computer Modelling, Vol. 28, No. 5, 1994, pp. 103-109.
[9] K. Abbaoui and Y. Cherruault, “New Ideas for Proving Convergence of Decomposition Methods,” Computers and Mathematics with Applications, Vol. 29, No. 7, 1995, pp. 103-108. doi:10.1016/0898-1221(95)00022-Q
[10] K. Abbaoui and Y. Cherruault, “Convergence of Adomian’s Method Applied to Nonlinear Equations,” Mathematical and Computer Modelling, Vol. 20, No. 9, 1994, pp. 60-73. doi:10.1016/0895-7177(94)00163-4
[11] Y. Cherruault and G. Adomian, “Decomposition Methods: a New Proof of Convergence,” Mathematical and Computer Modelling, Vol. 18, No. 12, 1993, pp. 103-106. doi:10.1016/0895-7177(93)90233-O
[12] S. Guellal and Y. Cherruault, “Practical Formula for Calculation of Adomian’s Polynomials and Application to the Convergence of the Decomposition Method,” International Journal Bio-Medical Computing, Vol. 36, No. 3, 1994, pp. 223-228. doi:10.1016/0020-7101(94)90057-4
[13] A. D. Polyanin and A. V. Manzhirov, “Handbook of Integral Equations,” CRC Press, New York, 1998. doi:10.1201/9781420050066
[14] A. J. Jerri, “Introduction to Integral Equations with Applications,” Wiley, New York, 1999.

  
comments powered by Disqus

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.