Approximate Series Solution of Nonlinear Singular Boundary Value Problems Arising in Physiology
We introduce an efficient recursive scheme based on Adomian decomposition method (ADM) for solving nonlinear singular boundary value problems. This approach is based on a modification of the ADM; here we use all the boundary conditions to derive an integral equation before establishing the recursive...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/945872 |
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| author | Randhir Singh Jitendra Kumar Gnaneshwar Nelakanti |
| author_facet | Randhir Singh Jitendra Kumar Gnaneshwar Nelakanti |
| author_sort | Randhir Singh |
| collection | DOAJ |
| description | We introduce an efficient recursive scheme based on Adomian decomposition
method (ADM) for solving nonlinear singular boundary value problems. This approach is based on a modification of the ADM; here we use all the boundary conditions to derive an integral equation before establishing the recursive scheme for the solution components. In fact, we develop the recursive scheme without any undetermined coefficients while computing the solution components. Unlike the classical ADM, the proposed method avoids solving a sequence of nonlinear algebraic or transcendental equations for the undetermined coefficients. The approximate solution is obtained in the form of series with easily calculable components. The uniqueness of the solution is discussed. The convergence and error
analysis of the proposed method are also established. The accuracy and reliability of the proposed method are examined by four numerical examples. |
| format | Article |
| id | doaj-art-bf581191c1f045c49bd22ee3d02ff853 |
| institution | Kabale University |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-bf581191c1f045c49bd22ee3d02ff8532025-02-03T01:21:51ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/945872945872Approximate Series Solution of Nonlinear Singular Boundary Value Problems Arising in PhysiologyRandhir Singh0Jitendra Kumar1Gnaneshwar Nelakanti2Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur 721302, IndiaDepartment of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur 721302, IndiaDepartment of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur 721302, IndiaWe introduce an efficient recursive scheme based on Adomian decomposition method (ADM) for solving nonlinear singular boundary value problems. This approach is based on a modification of the ADM; here we use all the boundary conditions to derive an integral equation before establishing the recursive scheme for the solution components. In fact, we develop the recursive scheme without any undetermined coefficients while computing the solution components. Unlike the classical ADM, the proposed method avoids solving a sequence of nonlinear algebraic or transcendental equations for the undetermined coefficients. The approximate solution is obtained in the form of series with easily calculable components. The uniqueness of the solution is discussed. The convergence and error analysis of the proposed method are also established. The accuracy and reliability of the proposed method are examined by four numerical examples.http://dx.doi.org/10.1155/2014/945872 |
| spellingShingle | Randhir Singh Jitendra Kumar Gnaneshwar Nelakanti Approximate Series Solution of Nonlinear Singular Boundary Value Problems Arising in Physiology The Scientific World Journal |
| title | Approximate Series Solution of Nonlinear Singular Boundary Value Problems Arising in Physiology |
| title_full | Approximate Series Solution of Nonlinear Singular Boundary Value Problems Arising in Physiology |
| title_fullStr | Approximate Series Solution of Nonlinear Singular Boundary Value Problems Arising in Physiology |
| title_full_unstemmed | Approximate Series Solution of Nonlinear Singular Boundary Value Problems Arising in Physiology |
| title_short | Approximate Series Solution of Nonlinear Singular Boundary Value Problems Arising in Physiology |
| title_sort | approximate series solution of nonlinear singular boundary value problems arising in physiology |
| url | http://dx.doi.org/10.1155/2014/945872 |
| work_keys_str_mv | AT randhirsingh approximateseriessolutionofnonlinearsingularboundaryvalueproblemsarisinginphysiology AT jitendrakumar approximateseriessolutionofnonlinearsingularboundaryvalueproblemsarisinginphysiology AT gnaneshwarnelakanti approximateseriessolutionofnonlinearsingularboundaryvalueproblemsarisinginphysiology |