Modified Adomian Techniques Applied to Non-Linear Volterra Integral Equations

DOI: 10.4236/ojapps.2013.32027   PDF   HTML   XML   3,416 Downloads   5,091 Views   Citations

Abstract

In this work, we studied the performance of modified techniques of Adomian method applied to non-linear Volterra integral equations of the second kind. This study shows that the modified techniques are reliable, efficient and easy to use through recursive relations that involve simple integrals. Furthermore, we found that the right choice and the proper implementation of the modified techniques reduce the computational difficulties and increase the speed of convergent, comparing with the standard Adomian method.

Share and Cite:

H. Ali and F. Abdelwahid, "Modified Adomian Techniques Applied to Non-Linear Volterra Integral Equations," Open Journal of Applied Sciences, Vol. 3 No. 2, 2013, pp. 202-207. doi: 10.4236/ojapps.2013.32027.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] H. Brunner, “Implicitly Linear Collocation Methods for Nonlinear Volterra Equations,” Applied Numerical Mathematics, Vol. 9, No. 3-5, 1992, pp. 235-247. doi:10.1016/0168-9274(92)90018-9
[2] T. Tang, S. McKee and T. Diogo, “Product Integration Methods for an Integral Equation with Logarithmic Singular Kernel,” Applied Numerical Mathematics, Vol. 9, No. 3-5, 1992, pp. 259-266. doi:10.1016/0168-9274(92)90020-E
[3] T. Diogo, S. McKee and T. Tang, “A Hermite-Type Col location Method for the Solution of an Integral Equation with a Certain Weakly Singular Kernel,” IMA Journal of Numerical Analysis, Vol. 11, No. 4, 1991, pp. 595-605. doi:10.1093/imanum/11.4.595
[4] G. Adomian, “The Decomposition Method for Nonlinear Dynamical Systems,” Journal of Mathematical Analysis and Applications, Vol. 120, No. 1, 1986, pp. 370-383. doi:10.1016/0022-247X(86)90223-4
[5] G. Adomian, “A Review of the Decomposition Method and Some Recent Results for Nonlinear Equations,” Mathematical and Computer Modeling, Vol. 13, No. 7, 1990, pp. 17-43. doi:10.1016/0895-7177(90)90125-7
[6] F. Abdelwahid, “A Mathematical Model of Adomian Polynomials,” Applied Mathematics and Computation, Vol. 141, No. 2-3, 2003, pp. 447-453. doi:10.1016/S0096-3003(02)00266-7
[7] F. Abdelwahid, “Adomian Decomposition Method Applied to Nonlinear Integral Equations,” Alexandria Journal of Mathematics, Vol. 1, No. 1, 2010, pp. 11-18.
[8] A. Wazwaz, “A Reliable Modification of Adomian De composition Method,” Applied Mathematics and Computation, Vol. 102, No. 1, 1999, pp. 77-86. doi:10.1016/S0096-3003(98)10024-3
[9] M. Hosseini, “Adomian Decomposition Method with Chebyshev Polynomials,” Applied Mathematics and Computation, Vol. 175, No. 2, 2006, pp. 1685-1693. doi:10.1016/j.amc.2005.09.014

  
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.