Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 3 (2008), 183 -- 193

MODIFIED ADOMIAN DECOMPOSITION METHOD FOR SINGULAR INITIAL VALUE PROBLEMS IN THE SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS

Yahya Qaid Hasan and Liu Ming Zhu

Abstract. In this paper an efficient modification of Adomian decomposition method is introduced for solving singular initial value problem in the second-order ordinary differential equations. The scheme is tested for some examples and the obtained results demonstrate efficiency of the proposed method.

2000 Mathematics Subject Classification: 65L05.
Keywords: Modified Adomian decomposition method; Singular ordinary differential equations.

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References

  1. G. Adomian, A review of the decomposition method and some recent results for nonlinear equation, Math. Comput. Modelling 13(7) (1990), 17-43. MR1071436(92h:00002a). Zbl 0713.65051.

  2. G. Adomian, Solving frontier problems of physics: The Decomposition Method, Kluwer, Boston, MA, 1994. MR1282283(95e:00026). Zbl 0802.65122.

  3. G. Adomian and R. Rach, Noise terms in decomposition series solution, Comput. Math. Appl. 24(11) (1992), 61-64. MR1186719. Zbl 0777.35018.

  4. G. Adomian, R. Rach and N.T. Shawagfeh, On the analytic solution of the Lane-Emden equation, Found. Phys. Lett. 8(2) (1995) 161-181.

  5. M. M. Hosseini, Adomian decomposition method with Chebyshev polynomials, Appl. Math. Comput. 175 (2006), 1685-1693. MR2225617. Zbl 1093.65073.

  6. R. Rach, A. Baghdasarian and G. Adomian, Differential coefficients with singular coefficients, Appl. Math. Comput. 47 (1992), 179-184. MR1143150(92i:34034). Zbl 0748.65066.

  7. A. M. Wazwaz, A First Course in Integral Equation, World Scientific, Singapore, 1997. MR1612107(99i:45001). Zbl 0924.45001.

  8. A. M. Wazwaz, A reliable modification of Adomian decomposition method, Appl. Math. Comput. 102 (1999), 77-86. MR1682855(99m:65156). Zbl 0928.65083.

  9. A. M. Wazwaz, Analytical approximations and Pade approximations for Volterra's population model, Appl. Math. Comput. 100 (1999), 13-25. MR1665900 Zbl 0953.92026.

  10. A. M. Wazwaz, A new algorithm for calculating Adomian polynomials for nonlinear operators, Appl. Math. Comput. 111(1) (2000), 53-69. MR1745908. Zbl 1023.65108.

  11. A. M. Wazwaz, A new method for solving singular initial value problems in the second-order ordinary differential equations, Appl. Math. Comput. 128 (2002), 45-57. MR1891179(2002m:34011). Zbl 1030.34004.



Yahya Qaid Hasan Liu Ming Zhu.
Department of Mathematics, Department of Mathematics,
Harbin Institute of Technology, Harbin Institute of Technology,
Harbin, 150001, Harbin, 150001,
P. R. China. P. R. China.
e-mail: yahya217@yahoo.com e-mail: mzliu@hit.edu.cn

http://www.utgjiu.ro/math/sma