An accurate numerical method for solving the linear fractional Klein-Gordon equation
In this article, an implementation of an efficient numerical method for solving the linear fractional Klein–Gordon equation (LFKGE) is introduced. The fractional derivative is described in the Caputo sense. The method is based upon a combination between the properties of the Chebyshev approximations...
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| Veröffentlicht in: | Mathematical methods in the applied sciences 2014-11, Vol.37 (18), p.2972-2979 |
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| container_title | Mathematical methods in the applied sciences |
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| creator | Khader, M.M. Kumar, Sunil |
| description | In this article, an implementation of an efficient numerical method for solving the linear fractional Klein–Gordon equation (LFKGE) is introduced. The fractional derivative is described in the Caputo sense. The method is based upon a combination between the properties of the Chebyshev approximations and finite difference method (FDM). The proposed method reduces LFKGE to a system of ODEs, which is solved using FDM. Special attention is given to study the convergence analysis and deduce an error upper bound of the proposed method. Numerical example is given to show the validity and the accuracy of the proposed algorithm. Copyright © 2013 John Wiley & Sons, Ltd. |
| doi_str_mv | 10.1002/mma.3035 |
| format | Article |
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The fractional derivative is described in the Caputo sense. The method is based upon a combination between the properties of the Chebyshev approximations and finite difference method (FDM). The proposed method reduces LFKGE to a system of ODEs, which is solved using FDM. Special attention is given to study the convergence analysis and deduce an error upper bound of the proposed method. Numerical example is given to show the validity and the accuracy of the proposed algorithm. 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Copyright © 2013 John Wiley & Sons, Ltd.</description><subject>Approximation</subject><subject>Chebyshev collocation method</subject><subject>Convergence</subject><subject>convergence analysis</subject><subject>Derivatives</subject><subject>Finite difference method</subject><subject>Fractional Klein-Gordon equation</subject><subject>Klein-Gordon equation</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Numerical analysis</subject><issn>0170-4214</issn><issn>1099-1476</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><recordid>eNp10EtLxDAQB_AgCq4P8CMEvHipTl59HJdFV1kfF194CWl2qtG20aRV99vbRVEUPAwDw49h5k_IDoN9BsAPmsbsCxBqhYwYFEXCZJaukhGwDBLJmVwnGzE-AkDOGB-Ry3FLjbV9MB3Stm8wOGtq2mD34Oe08oFGX7-69p52D0hr16IJtArGds63A5zV6Npk6sPctxRferOcb5G1ytQRt7_6Jrk6OrycHCenF9OTyfg0sVJIlUhryqGGK0uRqxIsT1UBgiOr0sxgAfNMVmpeMWEKgLTAlJsyy_KSq7KSqRGbZO9z73PwLz3GTjcuWqxr06Lvo2ap5DzPOaiB7v6hj74PwwdLxZXKBQPxs9AGH2PASj8H15iw0Az0Ml49xKuX8Q40-aRvrsbFv06fnY1_exc7fP_2JjzpNBOZ0jfnU303gfPZ5JrpW_EB2--JuQ</recordid><startdate>201411</startdate><enddate>201411</enddate><creator>Khader, M.M.</creator><creator>Kumar, Sunil</creator><general>Blackwell Publishing Ltd</general><general>Wiley Subscription Services, Inc</general><scope>BSCLL</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope></search><sort><creationdate>201411</creationdate><title>An accurate numerical method for solving the linear fractional Klein-Gordon equation</title><author>Khader, M.M. ; Kumar, Sunil</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c4345-4cab4ca099b385b0c2659032e1f67ae90d74f5df13a90069e62ab778b25bf46a3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>Approximation</topic><topic>Chebyshev collocation method</topic><topic>Convergence</topic><topic>convergence analysis</topic><topic>Derivatives</topic><topic>Finite difference method</topic><topic>Fractional Klein-Gordon equation</topic><topic>Klein-Gordon equation</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Numerical analysis</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Khader, M.M.</creatorcontrib><creatorcontrib>Kumar, Sunil</creatorcontrib><collection>Istex</collection><collection>CrossRef</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><jtitle>Mathematical methods in the applied sciences</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Khader, M.M.</au><au>Kumar, Sunil</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>An accurate numerical method for solving the linear fractional Klein-Gordon equation</atitle><jtitle>Mathematical methods in the applied sciences</jtitle><addtitle>Math. 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| language | eng |
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| source | Wiley Online Library |
| subjects | Approximation Chebyshev collocation method Convergence convergence analysis Derivatives Finite difference method Fractional Klein-Gordon equation Klein-Gordon equation Mathematical analysis Mathematical models Numerical analysis |
| title | An accurate numerical method for solving the linear fractional Klein-Gordon equation |
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