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Zbl 1242.65151
Do, Younghae; Jang, Bongsoo
Enhanced multistage differential transform method: application to the population models. (English)
[J] Abstr. Appl. Anal. 2012, Article ID 253890, 14 p. (2012). ISSN 1085-3375; ISSN 1687-0409/e

Summary: 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).

MSC 2000:: *65L99 Numerical methods for ODE
34A99 General theory of ODE
92D25 Population dynamics

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