COMPARISON DIFFERENTIAL TRANSFORM METHOD WITH ADOMIAN DECOMPOSITION METHOD FOR NONLINEAR INITIAL VALUE PROBLEMS
0
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
This paper present a numerical comparison between the differential transformation method (DTM) and Adomian decomposition method (ADM) for solving nonlinear dispersive K(m,n) equation. In order to show the effectiveness of the DTM, the results obtained from the DTM is compared with available solutions obtained using the ADM and with exact solutions. It illustrates the validity and the great potential of the differential transform method in solving nonlinear partial differential equations.
Abstract
This paper present a numerical comparison between the differential transformation method (DTM) and Adomian decomposition method (ADM) for solving nonlinear dispersive K(m,n) equation. In order to show the effectiveness of the DTM, the results obtained from the DTM is compared with available solutions obtained using the ADM and with exact solutions. It illustrates the validity and the great potential of the differential transform method in solving nonlinear partial differential equations.
참고문헌 (17)
- G. Adomian, "Nonlinear Stochastic Oprator Equations" (1986), Academic Press
- G. Adomian, "A review of the decomposition method and some recent results for non-linear equation", Math. Comput. Model, 13(7), pp.17~43 (1990)
- G. Adomian, "Equality of partial solutions in the decomposition method for linear or nonlinear partial differential equations", Comput. Math. Appl, 19(12), pp.9~12 (1990)
- G. Adomian, "Solution of physical problems by decomposition", Comput. Math. Appl, 27(9, pp.10) (1994), 145~154
- F. Ayaz, "On two-dimensional differential transform method", Appl. Math. Comput, 143, pp.361~374 (2003)
- C.K. Chen, "Solving partial differential equations by two-dimensional differ-ential transform method", Appl. Math. Compu, 106, pp.171~179 (1999)
- A.H. Hassan, "Different applications fort he differential transformation in the differ-ential equations", Appl. Math. Comput, 129, pp.183~201 (2002)
- A.H. Hassan, "Comparison differential transform technique with Adomian decomposi-tion method for linear and nonlinear initial value problems", Chaos, Soliton&Fractals, 36, pp.53~65 (2008)
- J.H. He, "Exp-function method for nonlinear wave equation", Chaos, Soli-tons&Fractals, 3013, pp.700~708 (2006)
- J.H. He, "Homotopy perturbation method for bifurcation of nonlinear problems", Int. J. Nonlinear Sci. Numer. Simul, 6, pp.207~208 (2005)
- J.H. He, "Some asymptotic methods for strongly nonlinear problems", Int. J. Moden Phys. B, 20(10), pp.1141~1199 (2006)
- J.H. He, "Application of homotopy perturbation method to nonlinear wave equations", Chaos, Solitons&Fractals, 26, pp.695~700 (2005)
- M.J. Jang, "Two-dimensional differential transform for partial differential equations", Appl. Math. Comput, 121, pp.261~270 (2001)
- P. Rosenau, "Compactons: solitons with finite wavelengths", Phys. Rev. Lett, 70(5), pp.564~567 (1993)
- A.M. Wazwaz, "New solitary wave special solutions with compact support fort he non-linear dispersive K(m,n) equations", Chaos, Solitons and Fractals, 13(22), pp.321~330 (2002)
- A.M. Wazwaz, "The variational iteration method for rational solutions for KdV, K(2,2), Burgers and cubic Boussinesq equations", Journal of Computational an Ap-plied Mathematics, 207, pp.18~23 (2007)
- J.K. Zhou, "Differential transformation and its application for electric circuits" (1986), Huajung University Pres