论文信息 - Application of differential transform method to non-linear oscillatory systems

Application of differential transform method to non-linear oscillatory systems

Abstract In this paper, the differential transform method is proposed for solving non-linear oscillatory systems. These solutions do not exhibit periodicity, which is the characteristic of oscillatory systems. A modification of the differential transform method, based on the use of Pade approximants, is proposed. We use alternative technique by which the solution obtained by the differential transform method is made periodic. The method is described and illustrated with examples. The results reveal that the method is very effective and convenient.

Moustafa El-Shahed | M. El-shahed

[1] S. G. Kelly. Comments on “A uniformly valid asympototic solution for d2ydt2 + y = a + ϵy2” , 1982 .

[2] K. Huseyin,et al. A note on “a uniformly valid asymptotic solution for d2y/dt2 + y = a + εy2” , 1982 .

[3] P. V. Woerkom. Comments on “A uniformly valid asymtotic, solution for d2ydt2 + y = a + ϵy2” , 1982 .

[4] Zhaosheng Feng,et al. Duffing's equation and its applications to the Hirota equation , 2003 .

[5] R. Mickens. A uniformly valid asymptotic solution for d2ydt2 + y = a + εy2☆ , 1981 .

[6] K. Rajalakshmi,et al. A modification of Adomian's solution for nonlinear oscillatory systems , 1995 .

[7] C. Dang,et al. An aftertreatment technique for improving the accuracy of Adomian's decomposition method , 2002 .

[8] Cha'o-Kuang Chen,et al. Application of differential transformation to eigenvalue problems , 1996 .

[9] L. Cvetićanin. Vibrations of the system with quadratic non-linearity and a constant excitation force , 2003 .