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Mahmoud S. Rawashdeh, Shehu Maitama. SOLVING NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS USING THE NDM[J]. Journal of Applied Analysis & Computation, 2015, 5(1): 77-88. doi: 10.11948/2015007
Citation: Mahmoud S. Rawashdeh, Shehu Maitama. SOLVING NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS USING THE NDM[J]. Journal of Applied Analysis & Computation, 2015, 5(1): 77-88. doi: 10.11948/2015007
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SOLVING NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS USING THE NDM

  • Department of Mathematics and Statistics, Jordan University of Science and Technology, P. O. Box 3030, Irbid 22110, Jordan

    Abstract
  • In this research paper, we examine a novel method called the Natural Decomposition Method (NDM). We use the NDM to obtain exact solutions for three different types of nonlinear ordinary differential equations (NLODEs). The NDM is based on the Natural transform method (NTM) and the Adomian decomposition method (ADM). By using the new method, we successfully handle some class of nonlinear ordinary differential equations in a simple and elegant way. The proposed method gives exact solutions in the form of a rapid convergence series. Hence, the Natural Decomposition Method (NDM) is an excellent mathematical tool for solving linear and nonlinear differential equation. One can conclude that the NDM is efficient and easy to use.
    MSC: 35Q61;44A10;44A15;44A20;44A30;44A35;81V10
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