The Multi-Step Differential Transform Method and Its Application to Determine the Solutions of Non-Linear Oscillators


Ertürk V. S., Odibat Z. M., Momani S.

ADVANCES IN APPLIED MATHEMATICS AND MECHANICS, vol.4, no.4, pp.422-438, 2012 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 4 Issue: 4
  • Publication Date: 2012
  • Doi Number: 10.4208/aamm.10-m1138
  • Journal Name: ADVANCES IN APPLIED MATHEMATICS AND MECHANICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.422-438
  • Keywords: Non-linear oscillatory systems, differential transform method, numerical solution, BOUNDARY-VALUE-PROBLEMS, EQUATIONS
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

In this paper, a reliable algorithm based on an adaptation of the standard differential transform method is presented, which is the multi-step differential transform method (MSDTM). The solutions of non-linear oscillators were obtained by MSDTM. Figurative comparisons between the MSDTM and the classical fourth-order Runge-Kutta method (RK4) reveal that the proposed technique is a promising tool to solve non-linear oscillators.