Approximate Solution of Two-Point Boundary Value Problems Using Adomian Decomposition Method with Green’s Function

Randhir Singh1, Gnaneshwar Nelakanti1, Jitendra Kumar1
1Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, India

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.

Tài liệu tham khảo

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