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New transform formulae for differential transformation methodwith applications to the nonlinear plane autonomous systems |
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| รหัสดีโอไอ | |
| Creator | 1. Uraiwan Somboon 2. Jaipong Kasemsuwan 3. Sorin V. Sabau |
| Title | New transform formulae for differential transformation methodwith applications to the nonlinear plane autonomous systems |
| Publisher | Research and Development Office, Prince of Songkla University |
| Publication Year | 2563 |
| Journal Title | Songklanakarin Journal of Science and Technology |
| Journal Vol. | 42 |
| Journal No. | 1 |
| Page no. | 81-94 |
| Keyword | differential transform method, nonlinear plane autonomous systems, multistep differential transform method, phase- plane method |
| URL Website | https://rdo.psu.ac.th/sjstweb/index.php |
| ISSN | 0125-3395 |
| Abstract | This work presents a new derivation technique for new differential transform formulae of a product of compositefunctions. The new formulae are applied to nonlinear plane autonomous systems to demonstrate their efficiency and reliability.The approximate series solutions estimated by the differential transform method (DTM) and the multistep differential transformmethod (MsDTM) are then compared with the flow direction of the vector fields defined by the original system and an analyticalsolution calculated by the phase-plane method. We found that the MsDTM results are in better agreement with the analyticalsolution than the DTM ones. Moreover, the MsDTM can be applied to systems whose analytical solutions are unobtainable. Theapproximate solutions by the MsDTM have the same direction to the flow of the vector field of the system. It follows that theproposed new formulae are reliable and efficient. |
