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Jang, Bongsoo

Two-point boundary value problems by the extended Adomian decomposition method. (English) Zbl 1145.65049

J. Comput. Appl. Math. 219, No. 1, 253-262 (2008).
Summary: We present an efficient numerical algorithm for solving two-point linear and nonlinear boundary value problems, which is based on the Adomian decomposition method (ADM), namely, the extended ADM. The proposed method is examined by comparing the results with other methods. Numerical results show that the proposed method is much more efficient and accurate than other methods with less computational work.

Cited in 21 Documents

MSC:

65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B05 Linear boundary value problems for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations

Keywords:

two-point boundary value problem; Adomian decomposition method; shooting methods; comparison of methods; numerical results
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\textit{B. Jang}, J. Comput. Appl. Math. 219, No. 1, 253--262 (2008; Zbl 1145.65049)
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References:

[1] Adomian, G., Solving frontier problems of physics: the decomposition method, (1994), Kluwer Academic Publications Dordrecht · Zbl 0802.65122
[2] Adomian, G.; Rach, R., Modified decomposition solution of linear and nonlinear boundary-value problems, Nonlinear anal., 23, 5, 615-619, (1994) · Zbl 0810.34015
[3] Benabidallah, M.; Cherruault, Y., Application of the adomain method for solving a class of boundary problems, Kybernetes, 33, 1, 118-132, (2004) · Zbl 1058.65075
[4] Caglar, H.; Caglar, N.; Elfaituri, K., B-spline interpolation compared with finite difference, finite element and finite volume methods which applied to two-point boundary value problems, Appl. math. comput., 175, 72-79, (2006) · Zbl 1088.65069
[5] Fang, Q.; Tsuchiya, T.; Yamamoto, T., Finite difference, finite element and finite volume methods applied to two-point boundary value problems, J. comput. appl. math., 139, 1, 9-19, (2002) · Zbl 0993.65082
[6] Ha, S.N., A nonlinear shooting method for two-point boundary value problems, Comput. math. appl., 42, 10-11, 1411-1420, (2001) · Zbl 0999.65077
[7] Inc, M.; Evans, D.J., The decomposition method for solving of a class of singular two-point boundary value problems, Int. J. comput. math., 80, 7, 869-882, (2003) · Zbl 1041.65060
[8] Jang, B., Exact solutions to one dimensional non-homogeneous parabolic problems by the homogeneous Adomian decomposition method, Appl. math. comput., 186, 969-979, (2007) · Zbl 1117.65140
[9] Jang, B., Solutions to the non-homogeneous parabolic problems by the extended HADM, Appl. math. comput., 191, 2, 466-483, (2007) · Zbl 1193.65182
[10] Keller, K., Numerical solutions of two-point boundary value problems, (1976), SIAM Philadelphia
[11] Taiwo, O.A., Exponential Fitting for the solution of two-point boundary value problems with cubic spline collocation tau-method, Int. J. comput. math., 79, 3, 299-306, (2002) · Zbl 0997.65096
[12] Wazwaz, A.M., A reliable algorithm for obtaining positive solutions for nonlinear boundary value problems, Comput. math. appl., 41, 1237-1244, (2001) · Zbl 0983.65090
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