Approximate Solution of Two-Point Boundary Value Problems Using Adomian Decomposition Method with Green’s Function
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences - Tập 85 - Trang 51-61 - 2014
Tóm tắt
In this paper, a new recursive scheme for solving Bratu’s type two-point boundary value problems is proposed. The recursive scheme is based on constructing Green’s function before establishing the recursive scheme for the solution components. Unlike Adomian decomposition method, this technique avoids solving a sequence of transcendental equations for the unknown constants. Approximations of the solution are obtained in the form of series with easily calculable components. Convergence analysis of series solution is established. The convergence analysis is reliable enough for estimating the maximum absolute error of series solution. Some example are included to demonstrate the accuracy, applicability, and generality of the proposed scheme.
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