A Novel Iterative Scheme and Its Application to Differential Equations
The purpose of this paper is to employ an alternative approach to reconstruct the standard variational iteration algorithm II proposed by He, including Lagrange multiplier, and to give a simpler formulation of Adomian decomposition and modified Adomian decomposition method in terms of newly proposed...
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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/10.1155/2014/605376 |
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| _version_ | 1850163222397583360 |
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| author | Yasir Khan F. Naeem Zdeněk Šmarda |
| author_facet | Yasir Khan F. Naeem Zdeněk Šmarda |
| author_sort | Yasir Khan |
| collection | DOAJ |
| description | The purpose of this paper is to employ an alternative approach to reconstruct the standard variational iteration algorithm II proposed by He, including Lagrange multiplier, and to give a simpler formulation of Adomian decomposition and modified Adomian decomposition method in terms of newly proposed variational iteration method-II (VIM). Through careful investigation of the earlier variational iteration algorithm and Adomian decomposition method, we find unnecessary calculations for Lagrange multiplier and also repeated calculations involved in each iteration, respectively. Several examples are given to verify the reliability and efficiency of the method. |
| format | Article |
| id | doaj-art-ebc81ccc73374fd18eca5f6c5a7a913c |
| institution | OA Journals |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-ebc81ccc73374fd18eca5f6c5a7a913c2025-08-20T02:22:20ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/605376605376A Novel Iterative Scheme and Its Application to Differential EquationsYasir Khan0F. Naeem1Zdeněk Šmarda2Department of Mathematics, Zhejiang University, Hangzhou 310027, ChinaModern Textile Institute, Donghua University, Shanghai 200051, ChinaDepartment of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technicka 8, 61600 Brno, Czech RepublicThe purpose of this paper is to employ an alternative approach to reconstruct the standard variational iteration algorithm II proposed by He, including Lagrange multiplier, and to give a simpler formulation of Adomian decomposition and modified Adomian decomposition method in terms of newly proposed variational iteration method-II (VIM). Through careful investigation of the earlier variational iteration algorithm and Adomian decomposition method, we find unnecessary calculations for Lagrange multiplier and also repeated calculations involved in each iteration, respectively. Several examples are given to verify the reliability and efficiency of the method.http://dx.doi.org/10.1155/2014/605376 |
| spellingShingle | Yasir Khan F. Naeem Zdeněk Šmarda A Novel Iterative Scheme and Its Application to Differential Equations The Scientific World Journal |
| title | A Novel Iterative Scheme and Its Application to Differential Equations |
| title_full | A Novel Iterative Scheme and Its Application to Differential Equations |
| title_fullStr | A Novel Iterative Scheme and Its Application to Differential Equations |
| title_full_unstemmed | A Novel Iterative Scheme and Its Application to Differential Equations |
| title_short | A Novel Iterative Scheme and Its Application to Differential Equations |
| title_sort | novel iterative scheme and its application to differential equations |
| url | http://dx.doi.org/10.1155/2014/605376 |
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