Solution of Second-Order IVP and BVP of Matrix Differential Models Using Matrix DTM
We introduce a matrix form of differential transformation method (DTM) and apply for nonlinear second-order initial value problems (IVPs) and boundary value problems (BVPs) of matrix models which are given by 𝐮(𝑡)=𝑓(𝑡,𝐮(𝑡),𝐮(𝑡)) and subject to initial conditions 𝐮(𝑎)=𝐮0,𝐮(𝑎)=𝐮1 and boundary cond...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/738346 |
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| author | Reza Abazari Adem Kılıcman |
| author_facet | Reza Abazari Adem Kılıcman |
| author_sort | Reza Abazari |
| collection | DOAJ |
| description | We introduce a matrix form of differential transformation method (DTM) and apply for nonlinear second-order initial value problems (IVPs) and boundary value problems (BVPs) of matrix models which are given by 𝐮(𝑡)=𝑓(𝑡,𝐮(𝑡),𝐮(𝑡)) and subject to initial conditions 𝐮(𝑎)=𝐮0,𝐮(𝑎)=𝐮1 and boundary conditions 𝐮(𝑎)=𝐮0,𝐮(𝑏)=𝐮1, where 𝐮0,𝐮1∈𝑅𝑟×𝑞. Also the convergence of present method is established. Several illustrative examples are given to demonstrate the effectiveness of the present method. |
| format | Article |
| id | doaj-art-3ddc79570ff743299e67007a02c71ab9 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-3ddc79570ff743299e67007a02c71ab92025-02-03T01:01:57ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/738346738346Solution of Second-Order IVP and BVP of Matrix Differential Models Using Matrix DTMReza Abazari0Adem Kılıcman1Young Researchers Club, Ardabil Branch, Islamic Azad University, P.O. Box 56169-54184, Ardabil, IranDepartment of Mathematics, Universiti Putra Malaysia (UPM), 43400, Serdang, MalaysiaWe introduce a matrix form of differential transformation method (DTM) and apply for nonlinear second-order initial value problems (IVPs) and boundary value problems (BVPs) of matrix models which are given by 𝐮(𝑡)=𝑓(𝑡,𝐮(𝑡),𝐮(𝑡)) and subject to initial conditions 𝐮(𝑎)=𝐮0,𝐮(𝑎)=𝐮1 and boundary conditions 𝐮(𝑎)=𝐮0,𝐮(𝑏)=𝐮1, where 𝐮0,𝐮1∈𝑅𝑟×𝑞. Also the convergence of present method is established. Several illustrative examples are given to demonstrate the effectiveness of the present method.http://dx.doi.org/10.1155/2012/738346 |
| spellingShingle | Reza Abazari Adem Kılıcman Solution of Second-Order IVP and BVP of Matrix Differential Models Using Matrix DTM Abstract and Applied Analysis |
| title | Solution of Second-Order IVP and BVP of Matrix Differential Models Using Matrix DTM |
| title_full | Solution of Second-Order IVP and BVP of Matrix Differential Models Using Matrix DTM |
| title_fullStr | Solution of Second-Order IVP and BVP of Matrix Differential Models Using Matrix DTM |
| title_full_unstemmed | Solution of Second-Order IVP and BVP of Matrix Differential Models Using Matrix DTM |
| title_short | Solution of Second-Order IVP and BVP of Matrix Differential Models Using Matrix DTM |
| title_sort | solution of second order ivp and bvp of matrix differential models using matrix dtm |
| url | http://dx.doi.org/10.1155/2012/738346 |
| work_keys_str_mv | AT rezaabazari solutionofsecondorderivpandbvpofmatrixdifferentialmodelsusingmatrixdtm AT ademkılıcman solutionofsecondorderivpandbvpofmatrixdifferentialmodelsusingmatrixdtm |