Abstract and Applied Analysis

Enhanced Multistage Differential Transform Method: Application to the Population Models

Younghae Do and Bongsoo Jang

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Abstract

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).

Article information

Source
Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 253890, 14 pages.

Dates
First available in Project Euclid: 1 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1364845145

Digital Object Identifier
doi:10.1155/2012/253890

Mathematical Reviews number (MathSciNet)
MR2926902

Zentralblatt MATH identifier
1242.65151

Citation

Do, Younghae; Jang, Bongsoo. Enhanced Multistage Differential Transform Method: Application to the Population Models. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 253890, 14 pages. doi:10.1155/2012/253890. https://projecteuclid.org/euclid.aaa/1364845145


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