Have a personal or library account? Click to login
Resolution of system of Volterra integral equations of the first kind by derivation technique and modified decomposition methods Cover

Resolution of system of Volterra integral equations of the first kind by derivation technique and modified decomposition methods

Open Access
|Dec 2020

References

  1. K. E. Atkinson, The Numerical Solution of Integral Equations of the Second Kind, Cambridge University Press, Cambridge, (1997).
  2. R. Kress, Linear Integral Equation. New York: Springer-Verlag (1998).
  3. P.K. Kythe and P. Puri, Computational methods for linear integral equations. Birkhauser Verlag, Springer, Boston, (2002).
  4. P. Linz, Analytical and Numerical Methods for Volterra Equations, SIAM, Philadelphia, (1985).
  5. B. Alpert, G. Beylkin, R. Coifman, V. Rokhlin, Waveletlike bases for the fast solution of second-kind integral equations, SIAM Journal on Scientific Computing, 14 (1993), 159-184.
  6. W.L. Golik, Wavelet packets for fast solution of electromagnetic integral equations, IEEE Trans. Ant. prop. 46 (1998), 618-624.
  7. E. Babolian, J. Biazar, and A.R. Vahidi, The decomposition method applied to system of Fredholm integral equations of the second kind, Appl. Math. Comput. 148 (2004), 443-452.
  8. J. Biazar, E. Babolian, R. Islam, Solution of the system of Volterra integral equations of the first kind by Adomian decomposition method, Appl. Math. Comput. 139 (2003), 249-258.
  9. H.O. Bakodah, Some modifications of Adomian decomposition method applied to nonlinear system of Fredholm integral equations of the second kind, International Journal of Contemporary Mathematical Sciences, 7(19), (2012), 929-942.
  10. H.O. Bakodah. A new modification of the Laplace Adomian decomposition method for system of integral equations, Journal of American Science, 8(10), (2012), 241-246.
  11. H.O. Bakodah, A comparison study between a Chebyshev collocation method and the Adomian decomposition method for solving linear system of Fredholm integral equations of the second kind, Journal of King Abdulaziz University:science, 24(1), (2012), 49-59.
  12. Y. Cherruault, V. Seng, The resolution of non-linear integral equations of the rst kind using the decompositional Method of Adomian, Kebernetes, 26(2), (1997), 198-206.
  13. E. Babolian, J. Biazar, Solution of a System of Nonlinear Volterra Integral Equations of the Second kind, Far East J. Math. Sci. 2(6), (2000), 935-945.
  14. J. Biazar, E. Babolian, R. Islam, Solution of a system of Volterra integral equations of the rst kind by Adomian method, Applied Mathematics and Computation, 139, (2003), 249-258.
  15. G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, Kluwer Academic Publishers, Boston, MA, (1994).
  16. A.M. Wazwaz, A reliable modication of the Adomian decomposition method, Appl. Math. Comput., 102 (1999), 77-86.
  17. A.M. Wazwaz and S. M. El-Sayed, A new modification of the Adomian decomposition method for linear and nonlinear operators, Applied Mathematics and Computation,122(3),(2001), 393-405.
  18. X. Lou, A two-step Adomian decomposition method, Appl. Math. Comput., 170, (2005), 570-583.
  19. H. Jafari, V. Daftardar-Gejji, Revised Adomian decomposition method for solving a system of nonlinear equations. Appl. Math. Comput., 175, (2006), 1-7.
  20. E. Babolian, S. Javadi, Restarted Adomian method for algebraic equations, Appl. Math. Comput., 146, (2003), 533-541.
  21. L. M. Delves and J.L. Mohamed, Computational method for integral equations, Cambridge university press, New York, NY. (1985).
  22. R. F. Churchous, Numerical Methods: Handbook of Applicable Mathematics, Vol III, (1981), spriner, New York, NY.
  23. A.M. Wazwaz, A comparison study between the modified decomposition method and the traditional methods for solving nonlinear integral equations, Applied Mathematics and Computation, 181 (2006), 1703-1712.
  24. A.M. Wazwaz, The modified decomposition method for analytic treatment of nonlinear integral equations and systems of nonlinear integral equations, International Journal of Computer Mathematics, 82(9), (2005), 1107-1115.
  25. H.S. Goghary, Sh. Javadi and E. Babolian, Restarted Adomian method for system of nonlinear Volterra integral equations, Appl. Math. Comput. 161 (2005), 745-751.
  26. R.I. Nuruddeen, L. Muhammad, A.M. Nass and T.A. Sulaiman, A review of the integral transforms-based decomposition methods and their applications in solving nonlinear PDEs, Palestine J. Math. 7, (2018), 262-280.
DOI: https://doi.org/10.2478/jamsi-2020-0007 | Journal eISSN: 1339-0015 | Journal ISSN: 1336-9180
Language: English
Page range: 23 - 38
Published on: Dec 24, 2020
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year

© 2020 M. A. Alzhrani, H. O. Bakodah, M. Al-Mazmumy, published by University of Ss. Cyril and Methodius in Trnava
This work is licensed under the Creative Commons Attribution 4.0 License.