Journal
COMPUTER PHYSICS COMMUNICATIONS
Volume 198, Issue -, Pages 97-104Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cpc.2015.09.006
Keywords
Bratu's problem; Green's functions; Fixed point iteration schemes; Boundary value problem
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In this article, the one-dimensional non-linear Bratu's boundary value problem is solved via a novel approach that combines Green's function and fixed point iterative schemes, such as Picard's and Krasnoselskii-Mann's. The convergence of the introduced iterative algorithm is proved using the contraction principle. The method is supported by considering a number of numerical examples that correspond to different cases of eigenvalues. The procedure underlying the strategy reduces calculations and provides highly accurate results in comparison with the exact solution and/or numerical solutions provided in the literature. The current method overcomes the difficulty of treating the problem for eigenvalues near and at the critical value, such as lambda = 3 and lambda = 3.51, and handles them reliably and very efficiently. (C) 2015 Elsevier B.V. All rights reserved.
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