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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| Vydáno v: | Mathematical methods in the applied sciences Ročník 40; číslo 18; s. 7396 - 7409 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Freiburg
Wiley Subscription Services, Inc
01.12.2017
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| ISSN: | 0170-4214, 1099-1476 |
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| Abstract | 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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| AbstractList | 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. |
| Author | Roul, Pradip |
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| SubjectTerms | 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 |
| Title | On the numerical solution of singular two‐point boundary value problems: A domain decomposition homotopy perturbation approach |
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