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Enhanced Multistage Differential Transform Method: Application to the Population Models

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  • Younghae Do
  • Bongsoo Jang

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).

Suggested Citation

  • Younghae Do & Bongsoo Jang, 2012. "Enhanced Multistage Differential Transform Method: Application to the Population Models," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:253890
    DOI: 10.1155/2012/253890
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    References listed on IDEAS

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    1. Kangalgil, Figen & Ayaz, Fatma, 2009. "Solitary wave solutions for the KdV and mKdV equations by differential transform method," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 464-472.
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    Cited by:

    1. Younghae Do & Bongsoo Jang, 2012. "Nonlinear Klein‐Gordon and Schrödinger Equations by the Projected Differential Transform Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    2. Noufe H. Aljahdaly & S. A. El-Tantawy, 2021. "On the Multistage Differential Transformation Method for Analyzing Damping Duffing Oscillator and Its Applications to Plasma Physics," Mathematics, MDPI, vol. 9(4), pages 1-12, February.
    3. S. S. Motsa & P. G. Dlamini & M. Khumalo, 2012. "Solving Hyperchaotic Systems Using the Spectral Relaxation Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).

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