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Open Engineering

formerly Central European Journal of Engineering

Editor-in-Chief: Ritter, William

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CiteScore 2017: 0.70

SCImago Journal Rank (SJR) 2017: 0.211
Source Normalized Impact per Paper (SNIP) 2017: 0.787

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2391-5439
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A reliable algorithm for positive solutions of nonlinear boundary value problems by the multistage Adomian decomposition method

Jun-Sheng Duan / Randolph Rach / Abdul-Majid Wazwaz
Published Online: 2014-11-27 | DOI: https://doi.org/10.1515/eng-2015-0007

Abstract

In this paper, we present a reliable algorithm to calculate positive solutions of homogeneous nonlinear boundary value problems (BVPs). The algorithm converts the nonlinear BVP to an equivalent nonlinear Fredholm– Volterra integral equation.We employ the multistage Adomian decomposition method for BVPs on two or more subintervals of the domain of validity, and then solve the matching equation for the flux at the interior point, or interior points, to determine the solution. Several numerical examples are used to highlight the effectiveness of the proposed scheme to interpolate the interior values of the solution between boundary points. Furthermore we demonstrate two novel techniques to accelerate the rate of convergence of our decomposition series solutions by increasing the number of subintervals and adjusting the lengths of subintervals in the multistage Adomian decomposition method for BVPs.

Keywords : boundary value problem; positive solution; Adomian decomposition method; multistage decomposition; nonlinear differential equation

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About the article

Received: 2014-10-19

Accepted: 2014-10-26

Published Online: 2014-11-27


Citation Information: Open Engineering, Volume 5, Issue 1, ISSN (Online) 2391-5439, DOI: https://doi.org/10.1515/eng-2015-0007.

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©2015 J.-S. Duan et al. . This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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