Further developments to the decomposition method for solving singular initial-value problems

Authors:
Afgan Aslanov;Ibrahim Abu-Alshaikh
Affiliations:
Fatih University, Department of Mathematics, 34500 Istanbul, Turkey;Department of Mechanical and Industrial Engineering, Applied Sciences University, 11931 Amman, Jordan
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2008

Citing 3
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Abstract

Singular initial-value problems in second-order ordinary differential equations of Lane-Emden type are investigated. In this study, we shall introduce a further development in the Adomian decomposition method to overcome the difficulty at the singular point of non-homogeneous, linear and non-linear Lane-Emden-like equations; especially when the singularity appears on the right-hand side of this type of equations. A more general concept of this type of initial-value problem is introduced with various examples. The numerical results of these examples are compared with exact solutions when available.