Superiority of legendre polynomials to Chebyshev polynomial in solving ordinary differential equation
In this paper, we proved the superiority of Legendre polynomial to Chebyshev polynomial in solving first order ordinary differential equation with rational coefficient. We generated shifted polynomial of Chebyshev, Legendre and Canonical polynomials which deal with solving differential equation by f...
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| Format: | Article |
| Language: | English |
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Joint Coordination Centre of the World Bank assisted National Agricultural Research Programme (NARP)
2006-11-01
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| Series: | Journal of Applied Sciences and Environmental Management |
| Online Access: | https://www.ajol.info/index.php/jasem/article/view/17365 |
| _version_ | 1797227654345129984 |
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| author | FO Akinpelu LA Adetunde EO Omidiora |
| author_facet | FO Akinpelu LA Adetunde EO Omidiora |
| author_sort | FO Akinpelu |
| collection | DOAJ |
| description | In this paper, we proved the superiority of Legendre polynomial to Chebyshev polynomial in solving first order ordinary differential equation with rational coefficient. We generated shifted polynomial of Chebyshev, Legendre and Canonical polynomials which deal with solving differential equation by first choosing Chebyshev polynomial T*n (X), defined with the help of hypergeometric series T*n (x) =F ( -n, n, ½ ;X) and later choosing Legendre polynomial P*n (x) define by the series P*n (x) = F ( -n, n+1, 1;X); with the help of an auxiliary set of Canonical polynomials Qk in order to find the superiority between the two polynomials. Numerical examples are given which show the superiority of Legendre polynomials to Chebyshev polynomials. Journal of Applied Sciences and Environmental Management Vol. 9(3) 2005: 121-124 |
| first_indexed | 2024-04-24T14:44:14Z |
| format | Article |
| id | doaj.art-ccd20f0e60354c31a82ad235b6154aad |
| institution | Directory Open Access Journal |
| issn | 2659-1502 2659-1499 |
| language | English |
| last_indexed | 2024-04-24T14:44:14Z |
| publishDate | 2006-11-01 |
| publisher | Joint Coordination Centre of the World Bank assisted National Agricultural Research Programme (NARP) |
| record_format | Article |
| series | Journal of Applied Sciences and Environmental Management |
| spelling | doaj.art-ccd20f0e60354c31a82ad235b6154aad2024-04-02T19:58:04ZengJoint Coordination Centre of the World Bank assisted National Agricultural Research Programme (NARP)Journal of Applied Sciences and Environmental Management2659-15022659-14992006-11-019310.4314/jasem.v9i3.17365Superiority of legendre polynomials to Chebyshev polynomial in solving ordinary differential equationFO AkinpeluLA AdetundeEO OmidioraIn this paper, we proved the superiority of Legendre polynomial to Chebyshev polynomial in solving first order ordinary differential equation with rational coefficient. We generated shifted polynomial of Chebyshev, Legendre and Canonical polynomials which deal with solving differential equation by first choosing Chebyshev polynomial T*n (X), defined with the help of hypergeometric series T*n (x) =F ( -n, n, ½ ;X) and later choosing Legendre polynomial P*n (x) define by the series P*n (x) = F ( -n, n+1, 1;X); with the help of an auxiliary set of Canonical polynomials Qk in order to find the superiority between the two polynomials. Numerical examples are given which show the superiority of Legendre polynomials to Chebyshev polynomials. Journal of Applied Sciences and Environmental Management Vol. 9(3) 2005: 121-124https://www.ajol.info/index.php/jasem/article/view/17365 |
| spellingShingle | FO Akinpelu LA Adetunde EO Omidiora Superiority of legendre polynomials to Chebyshev polynomial in solving ordinary differential equation Journal of Applied Sciences and Environmental Management |
| title | Superiority of legendre polynomials to Chebyshev polynomial in solving ordinary differential equation |
| title_full | Superiority of legendre polynomials to Chebyshev polynomial in solving ordinary differential equation |
| title_fullStr | Superiority of legendre polynomials to Chebyshev polynomial in solving ordinary differential equation |
| title_full_unstemmed | Superiority of legendre polynomials to Chebyshev polynomial in solving ordinary differential equation |
| title_short | Superiority of legendre polynomials to Chebyshev polynomial in solving ordinary differential equation |
| title_sort | superiority of legendre polynomials to chebyshev polynomial in solving ordinary differential equation |
| url | https://www.ajol.info/index.php/jasem/article/view/17365 |
| work_keys_str_mv | AT foakinpelu superiorityoflegendrepolynomialstochebyshevpolynomialinsolvingordinarydifferentialequation AT laadetunde superiorityoflegendrepolynomialstochebyshevpolynomialinsolvingordinarydifferentialequation AT eoomidiora superiorityoflegendrepolynomialstochebyshevpolynomialinsolvingordinarydifferentialequation |