On the numerical solution of singular two‐point boundary value problems: A domain decomposition homotopy perturbation approach

This paper reports a modified homotopy perturbation algorithm, called the domain decomposition homotopy perturbation method (DDHPM), for solving two‐point singular boundary value problems arising in science and engineering. The essence of the approach is to split the domain of the problem into a num...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences Vol. 40; no. 18; pp. 7396 - 7409
Main Author: Roul, Pradip
Format: Journal Article
Language:English
Published: Freiburg Wiley Subscription Services, Inc 01.12.2017
Subjects:
Boundary value problems
Decomposition
Domain decomposition methods
homotopy perturbation method
Integral equations
isothermal gas sphere
Iterative methods
Perturbation methods
singular boundary value problem
thermal explosion problem
ISSN:0170-4214, 1099-1476
Online Access:Get full text
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Summary:This paper reports a modified homotopy perturbation algorithm, called the domain decomposition homotopy perturbation method (DDHPM), for solving two‐point singular boundary value problems arising in science and engineering. The essence of the approach is to split the domain of the problem into a number of nonoverlapping subdomains. In each subdomain, a method based on a combination of HPM and integral equation formalism is implemented. The boundary condition at the right endpoint of each inner subdomain is established before deriving an iterative scheme for the components of the solution series. The accuracy and efficiency of the DDHPM are demonstrated by 4 examples (2 nonlinear and 2 linear). In comparison with the traditional HPM, the proposed domain decomposition HPM is highly accurate.
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ISSN:0170-4214
1099-1476
DOI:10.1002/mma.4536