Nonlinear Klein-Gordon and Schrödinger Equations by the Projected Differential Transform Method
The differential transform method (DTM) is based on the Taylor series for all variables, but it differs from the traditional Taylor series in calculating coefficients. Even if the DTM is an effective numerical method for solving many nonlinear partial differential equations, there are also some diff...
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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/10.1155/2012/150527 |
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| _version_ | 1850167676679225344 |
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| author | Younghae Do Bongsoo Jang |
| author_facet | Younghae Do Bongsoo Jang |
| author_sort | Younghae Do |
| collection | DOAJ |
| description | The differential transform method (DTM) is based on the Taylor series for all variables, but it differs from the traditional Taylor series in calculating coefficients. Even if the DTM is an effective numerical method for solving many nonlinear partial differential equations, there are also some difficulties due to the complex nonlinearity. To overcome difficulties arising in DTM, we present the new modified version of DTM, namely, the projected differential transform method (PDTM), for solving nonlinear partial differential equations. The proposed method is applied to solve the various nonlinear Klein-Gordon and Schrödinger equations. Numerical approximations performed by the PDTM are presented and compared with the results obtained by other numerical methods. The results reveal that PDTM is a simple and effective numerical algorithm. |
| format | Article |
| id | doaj-art-e76732ffefa6443b93299997d6793238 |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-e76732ffefa6443b93299997d67932382025-08-20T02:21:09ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/150527150527Nonlinear Klein-Gordon and Schrödinger Equations by the Projected Differential Transform MethodYounghae Do0Bongsoo Jang1Department of Mathematics, Kyungpook National University, Daegu 702-701, Republic of KoreaUlsan National Institute of Science and Technology (UNIST), Ulsan Metropolitan City 689-798, Republic of KoreaThe differential transform method (DTM) is based on the Taylor series for all variables, but it differs from the traditional Taylor series in calculating coefficients. Even if the DTM is an effective numerical method for solving many nonlinear partial differential equations, there are also some difficulties due to the complex nonlinearity. To overcome difficulties arising in DTM, we present the new modified version of DTM, namely, the projected differential transform method (PDTM), for solving nonlinear partial differential equations. The proposed method is applied to solve the various nonlinear Klein-Gordon and Schrödinger equations. Numerical approximations performed by the PDTM are presented and compared with the results obtained by other numerical methods. The results reveal that PDTM is a simple and effective numerical algorithm.http://dx.doi.org/10.1155/2012/150527 |
| spellingShingle | Younghae Do Bongsoo Jang Nonlinear Klein-Gordon and Schrödinger Equations by the Projected Differential Transform Method Abstract and Applied Analysis |
| title | Nonlinear Klein-Gordon and Schrödinger Equations by the Projected Differential Transform Method |
| title_full | Nonlinear Klein-Gordon and Schrödinger Equations by the Projected Differential Transform Method |
| title_fullStr | Nonlinear Klein-Gordon and Schrödinger Equations by the Projected Differential Transform Method |
| title_full_unstemmed | Nonlinear Klein-Gordon and Schrödinger Equations by the Projected Differential Transform Method |
| title_short | Nonlinear Klein-Gordon and Schrödinger Equations by the Projected Differential Transform Method |
| title_sort | nonlinear klein gordon and schrodinger equations by the projected differential transform method |
| url | http://dx.doi.org/10.1155/2012/150527 |
| work_keys_str_mv | AT younghaedo nonlinearkleingordonandschrodingerequationsbytheprojecteddifferentialtransformmethod AT bongsoojang nonlinearkleingordonandschrodingerequationsbytheprojecteddifferentialtransformmethod |