Natural Decomposition Approximation Solution for First Order Nonlinear Differential Equations
-
2018-09-22 https://doi.org/10.14419/ijet.v7i4.5.20202 -
Adomian polynomial, Logistic Equation, Natural transform, sumudu transforms. -
Abstract
In this research paper, we propose the Natural decomposition method (NDM) to solve nonlinear first order differential equations. We compare the results obtained by NDM with the exact solutions. This method is a combination of the natural transform method and adomian decomposition method. By showing the less error one can be concluded that the NDM is easy to use and efficient.
Â
Â
-
References
[1] Z. H. Khan and W.A. Khan, “N-transform properties and applicationsâ€, NUST Journal of Engg. Sciences, vol 1, 2008, pp. 127-133.
[2] Mahmoud S., Rawashdeh and S Maitama, “Solving nonlinear ordinary differential equations using the NDMâ€, Journal of Applied Analysis and Computation, vol. 5 ED-1, 2015, pp. 77-88.
[3] Mahmoud S., S Maitama, “Solving coupled system of nonlinear pde’s using the natural decomposition methodâ€, International journal of pure and applied mathematics, vol. 92 ED-5, 2014, pp. 757-776.
[4] Chun C.,H. Jafari and Y.I. Kim, “Numerical method for the wave and nonlinear diffusion equations with homotopy perturbation method,†Computational mathematics Applications, vol. 57, 2009, pp. 1226-1231.
[5] J. Singh, D. Kumar, and Sushila, “Homotopy perturbation Sumudu transform method for nonlinear equationsâ€, Advances in Applied Mathematics and Mechanics, vol. 4, 2011, pp. 165-175.
[6] G.K. Watugala, “The Sumudu transform for functions of two variables,†Math. Eng. Ind., vol. 8, 2001, pp. 293-302.
[7] P. Vadasza, S. Olekb, “Convergence and accuracy of Adomian’s decomposition method for the solution of Lorenz equationsâ€, International Journal of Heat Mass Transfer, vol. 43, 2000, pp. 1715-1734.
[8] A. Ghorbani, “Beyond Adomian’s polynomials: He polynomialsâ€, Chaos, Solitons & Fractals, vol. 39, 2009, pp. 1486-1492.
[9] S. Saha Ray and A. Patra, “Application of Homotopy Analysis Method and Adomian Decomposition Method for the Solution of Neutron Diffusion Equation in the Hemisphere and Cylindrical Reactorsâ€, Journal of Nuclear Engineering and Technology, vol. 1,2011, D-2-3, pp. 1-12.
[10] A. Patra, S. Saha Ray, “Aomian Approximation Solution for Fractional Order Riccati Differential Equation,†Mathematical Sciences International Research Journal, vol. 2, 2013, pp.245-249.
-
Downloads
-
How to Cite
Patra, A., T. Shone, T., & B. Mishra, B. (2018). Natural Decomposition Approximation Solution for First Order Nonlinear Differential Equations. International Journal of Engineering & Technology, 7(4.5), 442-445. https://doi.org/10.14419/ijet.v7i4.5.20202Received date: 2018-09-24
Accepted date: 2018-09-24
Published date: 2018-09-22