Newfangled Linearization Formula of Certain Nonsymmetric Jacobi Polynomials: Numerical Treatment of Nonlinear Fisher’s Equation
This article is devoted to deriving a new linearization formula of a class for Jacobi polynomials that generalizes the third-kind Chebyshev polynomials class. In fact, this new linearization formula generalizes some existing ones in the literature. The derivation of this formula is based on employin...
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| Format: | Article |
| Language: | English |
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Wiley
2023-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2023/6833404 |
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| author | W. M. Abd-Elhameed Afnan Ali Y. H. Youssri |
| author_facet | W. M. Abd-Elhameed Afnan Ali Y. H. Youssri |
| author_sort | W. M. Abd-Elhameed |
| collection | DOAJ |
| description | This article is devoted to deriving a new linearization formula of a class for Jacobi polynomials that generalizes the third-kind Chebyshev polynomials class. In fact, this new linearization formula generalizes some existing ones in the literature. The derivation of this formula is based on employing a new moment formula of this class of polynomials and after that using suitable symbolic computation to reduce the resulting linearization coefficients into simplified forms that do not contain any hypergeometric functions or sums. The new formula is employed along with some other formulas and with the utilization of the spectral tau method to obtain numerical solutions to the nonlinear Fisher equation. The presented method is used to convert the equation governed by its underlying conditions into a nonlinear system of equations. The solution of the resulting system can be obtained through any suitable standard numerical scheme. To demonstrate the efficiency and usefulness of the proposed algorithm, some examples are shown, including comparisons with some existing techniques in the literature. |
| format | Article |
| id | doaj-art-74d771bbf4914b26b3caebe5e34e176c |
| institution | Kabale University |
| issn | 2314-8888 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-74d771bbf4914b26b3caebe5e34e176c2025-02-03T06:48:32ZengWileyJournal of Function Spaces2314-88882023-01-01202310.1155/2023/6833404Newfangled Linearization Formula of Certain Nonsymmetric Jacobi Polynomials: Numerical Treatment of Nonlinear Fisher’s EquationW. M. Abd-Elhameed0Afnan Ali1Y. H. Youssri2Department of MathematicsDepartment of MathematicsDepartment of MathematicsThis article is devoted to deriving a new linearization formula of a class for Jacobi polynomials that generalizes the third-kind Chebyshev polynomials class. In fact, this new linearization formula generalizes some existing ones in the literature. The derivation of this formula is based on employing a new moment formula of this class of polynomials and after that using suitable symbolic computation to reduce the resulting linearization coefficients into simplified forms that do not contain any hypergeometric functions or sums. The new formula is employed along with some other formulas and with the utilization of the spectral tau method to obtain numerical solutions to the nonlinear Fisher equation. The presented method is used to convert the equation governed by its underlying conditions into a nonlinear system of equations. The solution of the resulting system can be obtained through any suitable standard numerical scheme. To demonstrate the efficiency and usefulness of the proposed algorithm, some examples are shown, including comparisons with some existing techniques in the literature.http://dx.doi.org/10.1155/2023/6833404 |
| spellingShingle | W. M. Abd-Elhameed Afnan Ali Y. H. Youssri Newfangled Linearization Formula of Certain Nonsymmetric Jacobi Polynomials: Numerical Treatment of Nonlinear Fisher’s Equation Journal of Function Spaces |
| title | Newfangled Linearization Formula of Certain Nonsymmetric Jacobi Polynomials: Numerical Treatment of Nonlinear Fisher’s Equation |
| title_full | Newfangled Linearization Formula of Certain Nonsymmetric Jacobi Polynomials: Numerical Treatment of Nonlinear Fisher’s Equation |
| title_fullStr | Newfangled Linearization Formula of Certain Nonsymmetric Jacobi Polynomials: Numerical Treatment of Nonlinear Fisher’s Equation |
| title_full_unstemmed | Newfangled Linearization Formula of Certain Nonsymmetric Jacobi Polynomials: Numerical Treatment of Nonlinear Fisher’s Equation |
| title_short | Newfangled Linearization Formula of Certain Nonsymmetric Jacobi Polynomials: Numerical Treatment of Nonlinear Fisher’s Equation |
| title_sort | newfangled linearization formula of certain nonsymmetric jacobi polynomials numerical treatment of nonlinear fisher s equation |
| url | http://dx.doi.org/10.1155/2023/6833404 |
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