A comparative study of Adomain decomposition method and the new integral transform “Elzaki transform’’

  • Authors

    • Badradeen Adam University of Khartoum, Faculty of Education - Depart. of Mathematics
    2014-12-13
    https://doi.org/10.14419/ijamr.v4i1.3799
  • Adomain Decomposition Method, Elzaki Transform, Linear Partial Differential Equation.

  • Abstract

    In this article, we present a comparative study between Adomain decomposition method and the new integral transform “Elzaki Transformâ€. We use the methods to solve the linear Partial differential equations with constant coefficients.

  • References

    1. [1] Kaya, D. and S.M. El-Sayed, 2003." On the solution of the coupled Schrödinger-KdV equation by the decomposition method". Physics Letters A., 313: 82-88. http://dx.doi.org/10.1016/S0375-9601 (03)00723-0.

      [2] Zhao, X., 2011." New Rational Formal Solutions of mKdV Equation". Appli. Math. Sci., 5:2187-2193.

      [3] Alazman, A.A., J.P. Albert, J.L. Bona, M. Chen and J. Wu, 2006." Comparisons between the BBMequation and a boussinesq system". Advances in Differential Equations. 11 (2): 121-166.

      [4] Burnsy, J., A. Balogh, D.S. Gilliamz and V.I. Shubovz, 1998. "Numerical Stationary Solutions for a Viscous Burgers' Equation". Journal of Mathematical Systems, Estimation and Control. 8 (2): 11-16.

      [5] Dogan, A.K., 2002. "Numerical solution of RLW equation using linear finite elements within Galerkin's method". Appl. Math. Model, 26 (7): 771-783. http://dx.doi.org/10.1016/S0307-904X(01)00084-1.

      [6] Hu, X.B. and Y.T. Wu, 1998." Application of the Hirota bilinear for malism to a new integrable differential-difference equation". Phys. Lett. A., 246: 523-529. http://dx.doi.org/10.1016/S0375-9601(98)00571-4.

      [7] Fan, E., 2000." Two new applications of the homogeneous balance method". Phys. Lett. A., 256: 353-357. http://dx.doi.org/10.1016/S0375-9601(00) 00010-4.

      [8] Wang, M., Y. Zhou and Z. Li, 1996. "Applications of a homogeneous balance method to exact solution of nonlinear equations in mathematical physics". Phys. Lett. A., 216: 67-75. http://dx.doi.org/10.1016/0375-9601(96)00283-6.

      [9] Vakhnenko, V.O., E.J. Parkes and A.J. Morrison, 2003." A Bäcklund transformation and the inversescattering transform method for the generalized Vakhnenko equation Chaos Solitons Fractals", 17: 683-692. http://dx.doi.org/10.1016/S0960-0779(02)00483-6.

      [10] He, J.H., 1998. "Approximate solution of nonlinear differential equations with convolution productnonlinearities Comput". Methods Appl. Mech. Eng., 167: 57-68 http://dx.doi.org/10.1016/S0045-7825(98)00108-X.

      [11] G. Adomian," A review of the decomposition method in applied mathematics", J. Math. Anal. Appl. 135 (1988) 501–544. http://dx.doi.org/10.1016/0022-247X(88)90170-9.

      [12] G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, Kluwer Academic Publishers, Boston, 1994. http://dx.doi.org/10.1007/978-94-015-8289-6.

      [13] A.M. Wazwaz, "Necessary conditions for the appearance of noise terms in decomposition solution series", Appl. Math. Comput. 81 (1997) 265–274. http://dx.doi.org/10.1016/S0096-3003(95)00327-4.

      [14] A.M.Wazwaz, A First Course in Integral Equations,World Scientific, Singapore, 1997. http://dx.doi.org/10.1142/3444.

      [15] A.M.Wazwaz, "Analytical approximations and Padé's approximants for Volterra's population model", Appl. Math. Comput. 100 (1999) 13–25. http://dx.doi.org/10.1016/S0096-3003(98)00018-6.

      [16] A.M.Wazwaz, "A new technique for calculating Adomian polynomials for nonlinear polynomials", Appl. Math. Comput. 111 (1) (2000) 33–51. http://dx.doi.org/10.1016/S0096-3003 (99)00063-6.

      [17] A.M.Wazwaz," A new algorithm for calculating Adomian polynomials for nonlinear operators", Appl. Math. And Comput. 111 (2000) 53–69. http://dx.doi.org/10.1016/S0096-3003 (99)00047-8.

      [18] A.M.Wazwaz, "The decomposition method for solving the diffusion equation subject to the classification of mass", Internat. J. Appl. Math. 3 (1) (2000) 25–34.

      [19] A.M.Wazwaz, Partial Differential Equations: Methods and Applications, Balkema Publishers, the Netherlands, 2002.

      [20] A.M.Wazwaz," A new method for solving singular initial value problems in the second order differential equations", Appl. Math. Comput. 128(2002) 47–57. http://dx.doi.org/10.1016/S0096-3003(01)00021-2.

      [21] Tarig M. Elzaki,"The New Integral Transform "Elzaki Transform" Global Journal of Pure and Applied Mathematics, ISSN 0973-1768, Number 1(2011), pp. 57-64.

      [22] Tarig M. Elzaki & Salih M. Elzaki," Application of New Transform "Elzaki Transform" to Partial Differential Equations", Global Journal of Pure and Applied Mathematics, ISSN 0973-1768,Number 1(2011), pp. 65-70.

      [23] Tarig M. Elzaki & Salih M. Elzaki,"On the Connections Between Laplace and Elzaki transforms", Advances in Theoretical and Applied Mathematics, ISSN 0973-4554 Volume 6, Number 1(2011),pp. 1-11.

      [24] Tarig M. Elzaki & Salih M. Elzaki,"On the Elzaki Transform and Ordinary Differential Equation with Variable Coefficients", Advances in Theoretical and Applied Mathematics. ISSN 0973-4554 Volume 6, Number 1(2011), pp. 13-18.

      [25] Tarig M. Elzaki, Adem Kilicman, Hassan Eltayeb." On Existence and Uniqueness of Generalized Solutions for a Mixed-Type Differential Equation", Journal of Mathematics Research, Vol. 2, No. 4 (2010) pp. 88-92.

      [26] Tarig M. Elzaki, "Existence and Uniqueness of Solutions for Composite Type Equation", Journal of Science and Technology, (2009). pp. 214-219.

  • Downloads

  • How to Cite

    Adam, B. (2014). A comparative study of Adomain decomposition method and the new integral transform “Elzaki transform’’. International Journal of Applied Mathematical Research, 4(1), 8-14. https://doi.org/10.14419/ijamr.v4i1.3799

    Received date: 2014-11-04

    Accepted date: 2014-12-03

    Published date: 2014-12-13