Numerical analysis for the Klein-Gordon equation with mass parameter
Abstract A numerical analysis of the well-known linear partial differential equation describing the relativistic wave is presented in this work. Three different operators of fractional differentiation with power law, exponential decay law and Mittag-Leffler law are employed to extend the Klein-Gordo...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2017-09-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-017-1352-6 |
| _version_ | 1819266246193971200 |
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| author | Badr Saad T Alkahtani Abdon Atangana Ilknur Koca |
| author_facet | Badr Saad T Alkahtani Abdon Atangana Ilknur Koca |
| author_sort | Badr Saad T Alkahtani |
| collection | DOAJ |
| description | Abstract A numerical analysis of the well-known linear partial differential equation describing the relativistic wave is presented in this work. Three different operators of fractional differentiation with power law, exponential decay law and Mittag-Leffler law are employed to extend the Klein-Gordon equation with mass parameter to the concept of fractional differentiation. The three models are solved numerically. The stability and the convergence of the numerical schemes are investigated in detail. |
| first_indexed | 2024-12-23T20:58:13Z |
| format | Article |
| id | doaj.art-d240f94ca0884938959f94b7f2e09fe2 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-23T20:58:13Z |
| publishDate | 2017-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-d240f94ca0884938959f94b7f2e09fe22022-12-21T17:31:27ZengSpringerOpenAdvances in Difference Equations1687-18472017-09-012017111310.1186/s13662-017-1352-6Numerical analysis for the Klein-Gordon equation with mass parameterBadr Saad T Alkahtani0Abdon Atangana1Ilknur Koca2Department of Mathematics, College of Science, King Saud UniversityInstitute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free StateDepartment of Mathematics, Faculty of Sciences, Mehmet Akif Ersoy UniversityAbstract A numerical analysis of the well-known linear partial differential equation describing the relativistic wave is presented in this work. Three different operators of fractional differentiation with power law, exponential decay law and Mittag-Leffler law are employed to extend the Klein-Gordon equation with mass parameter to the concept of fractional differentiation. The three models are solved numerically. The stability and the convergence of the numerical schemes are investigated in detail.http://link.springer.com/article/10.1186/s13662-017-1352-6second approximation of fractional derivativeKlein-Gordon equationstability analysis |
| spellingShingle | Badr Saad T Alkahtani Abdon Atangana Ilknur Koca Numerical analysis for the Klein-Gordon equation with mass parameter Advances in Difference Equations second approximation of fractional derivative Klein-Gordon equation stability analysis |
| title | Numerical analysis for the Klein-Gordon equation with mass parameter |
| title_full | Numerical analysis for the Klein-Gordon equation with mass parameter |
| title_fullStr | Numerical analysis for the Klein-Gordon equation with mass parameter |
| title_full_unstemmed | Numerical analysis for the Klein-Gordon equation with mass parameter |
| title_short | Numerical analysis for the Klein-Gordon equation with mass parameter |
| title_sort | numerical analysis for the klein gordon equation with mass parameter |
| topic | second approximation of fractional derivative Klein-Gordon equation stability analysis |
| url | http://link.springer.com/article/10.1186/s13662-017-1352-6 |
| work_keys_str_mv | AT badrsaadtalkahtani numericalanalysisforthekleingordonequationwithmassparameter AT abdonatangana numericalanalysisforthekleingordonequationwithmassparameter AT ilknurkoca numericalanalysisforthekleingordonequationwithmassparameter |