Journal
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
Volume 38, Issue 1, Pages 271-287Publisher
SPRINGER
DOI: 10.1007/s40840-014-0018-8
Keywords
Reproducing kernel method; Series solutions; Bratu's problem; Reproducing kernel space
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Funding
- Firat University Scientific Research Projects Unit, Turkey is under the Research University Grant Scheme [FF.12.09]
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In this paper, we use the reproducing kernel Hilbert space method for solving a boundary value problem for the second order Bratu's differential equation. Convergence analysis of presented method is discussed. The numerical approximations to the exact solution are computed and compared with other existing methods. Our presented method produces more accurate results in comparison with those obtained by Adomian decomposition, Laplace decomposition, B-spline, non-polynomial spline and Lie-group shooting methods. Our yardstick is absolute error. The comparison of the results with exact ones is made to confirm the validity and efficiency.
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