The Adomian Decomposition Method with Discretization for Second Order Initial Value Problems

Penulis

  • Dagnachew Mengstie Tefera Department of Mathematics, Debre Tabor University
  • Awoke Andargie Department of Mathematics, Bahir Dar University

Kata Kunci:

Decomposition method, Adomian polynomial, initial value problems, infinite series

Abstrak

In this paper, Adomian Decomposition Method with Discretization (ADMD) is applied to solve both linear and nonlinear initial value problems (IVP). Comparison with Adomian Decomposition Method (ADM) is presented. To illustrate the efficiency and accuracy of the method, five examples are considered. The result shows that ADMD is more efficient and accurate than ADM.

Referensi

G. Adomian, “A review of the decomposition method in applied mathematics,” Journal of mathematical analysis and applications, vol. 135, no. 2, pp. 501–544, 1988.

K. Al-Khaled and M. Anwar, “Numerical comparison of methods for solving second-order ordinary initial value problems,” Applied Mathematical Modelling, vol. 31, no. 2, pp. 292–301, 2007.

A. Elsaid, “Adomian polynomials: A powerful tool for iterative methods of series solution of nonlinear equations,” Journal of Applied Analysis and Computation, vol. 2, no. 4, pp. 381–394, 2015.

M. Al-Mazmumy, A. Al-Mutairi, and K. Al-Zahrani, “An efficient decomposition method for solving bratu’s boundary value problem,” American Journal of Computational Mathematics, vol. 7, no. 01, pp. 84–93, 2017.

G. Nhawu, P. Mafuta, and J. Mushanyu, “The adomian decomposition method for numerical solution of first-order differential equations,” Journal of Mathematical and Computational Science, vol. 6, no. 3, pp. 307–314, 2016.

E. Agom, “Application of adomian decomposition method in solving second order nonlinear ordinary differential equations,” International Journal of Engineering Science Invention, vol. 4, pp. 60–65, 11 2015.

H. Alkresheh, “New classes of adomian polynomials for the adomian decomposition method,” International Journal of Engineering Science Invention, vol. 5, no. 3, pp. 37–44, 2016.

A.-M. Wazwaz, “A comparison between adomian decomposition method and taylor series method in the series solutions,” Applied Mathematics and Computation, vol. 97, no. 1, pp. 37–44, 1998.

J. Edwards, J. Roberts, and N. Ford, “A comparison of adomian’s decomposition method and runge kutta methods for approximate solution of some predator prey model equations,” 1997.

K. Abbaoui and Y. Cherruault, “Convergence of adomian’s method applied to differential equations,” Computers & Mathematics with Applications, vol. 28, no. 5, pp. 103–109, 1994.

K. Abbaoui and Y. Cherruault, “Convergence of adomian’s method applied to nonlinear equations,” Mathematical and Computer Modelling, vol. 20, no. 9, pp. 69–73, 1994.

Diterbitkan

2019-11-15

Cara Mengutip

Tefera, D. M., & Andargie, A. (2019). The Adomian Decomposition Method with Discretization for Second Order Initial Value Problems. (IJCSAM) International Journal of Computing Science and Applied Mathematics, 5(2), 56–60. Diambil dari https://journal.its.ac.id/index.php/ijcsam/article/view/4647

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