Enhanced Multistage Differential Transform Method: Application to the Population Models
We present an efficient computational algorithm, namely, the enhanced multistage differential transform method (E-MsDTM) for solving prey-predator systems. Since the differential transform method (DTM) is based on the Taylor series, it is difficult to obtain accurate approximate solutions in large d...
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Online Access: | http://dx.doi.org/10.1155/2012/253890 |
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doaj-969e7d1e6c9e4a049763960d9ded9bee2020-11-24T21:31:39ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/253890253890Enhanced Multistage Differential Transform Method: Application to the Population ModelsYounghae Do0Bongsoo Jang1Department of Mathematics, Kyungpook National University, Daegu 702-701, Republic of KoreaUlsan National Institute of Science and Technology (UNIST), Ulsan Metropolitan City 689-798, Republic of KoreaWe present an efficient computational algorithm, namely, the enhanced multistage differential transform method (E-MsDTM) for solving prey-predator systems. Since the differential transform method (DTM) is based on the Taylor series, it is difficult to obtain accurate approximate solutions in large domain. To overcome this difficulty, the multistage differential transform method (MsDTM) has been introduced and succeeded to have reliable approximate solutions for many problems. In MsDTM, it is the key to update an initial condition in each subdomain. The standard MsDTM utilizes the approximate solution directly to assign the new initial value. Because of local convergence of the Taylor series, the error is accumulated in a large domain. In E-MsDTM, we propose the new technique to update an initial condition by using integral operator. To demonstrate efficiency of the proposed method, several numerical tests are performed and compared with ones obtained by other numerical methods such as MsDTM, multistage variational iteration method (MVIM), and fourth-order Runge-Kutta method (RK4).http://dx.doi.org/10.1155/2012/253890 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Younghae Do Bongsoo Jang |
spellingShingle |
Younghae Do Bongsoo Jang Enhanced Multistage Differential Transform Method: Application to the Population Models Abstract and Applied Analysis |
author_facet |
Younghae Do Bongsoo Jang |
author_sort |
Younghae Do |
title |
Enhanced Multistage Differential Transform Method: Application to the Population Models |
title_short |
Enhanced Multistage Differential Transform Method: Application to the Population Models |
title_full |
Enhanced Multistage Differential Transform Method: Application to the Population Models |
title_fullStr |
Enhanced Multistage Differential Transform Method: Application to the Population Models |
title_full_unstemmed |
Enhanced Multistage Differential Transform Method: Application to the Population Models |
title_sort |
enhanced multistage differential transform method: application to the population models |
publisher |
Hindawi Limited |
series |
Abstract and Applied Analysis |
issn |
1085-3375 1687-0409 |
publishDate |
2012-01-01 |
description |
We present an efficient computational algorithm, namely, the enhanced multistage differential transform method (E-MsDTM) for solving prey-predator systems. Since the differential transform method (DTM) is based on the Taylor series, it is difficult to obtain accurate approximate solutions in large domain. To overcome this difficulty, the multistage differential transform method (MsDTM) has been introduced and succeeded to have reliable approximate solutions for many problems. In MsDTM, it is the key to update an initial condition in each subdomain. The standard MsDTM utilizes the approximate solution directly to assign the new initial value. Because of local convergence of the Taylor series, the error is accumulated in a large domain. In E-MsDTM, we propose the new technique to update an initial condition by using integral operator. To demonstrate efficiency of the proposed method, several numerical tests are performed and compared with ones obtained by other numerical methods such as MsDTM, multistage variational iteration method (MVIM), and fourth-order Runge-Kutta method (RK4). |
url |
http://dx.doi.org/10.1155/2012/253890 |
work_keys_str_mv |
AT younghaedo enhancedmultistagedifferentialtransformmethodapplicationtothepopulationmodels AT bongsoojang enhancedmultistagedifferentialtransformmethodapplicationtothepopulationmodels |
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1725960425280897024 |