An Efficient Zero-Stable Numerical Method for Fourth-Order Differential Equations
The purpose of this paper is to produce an efficient zero-stable numerical method with the same order of accuracy as that of the main starting values (predictors) for direct solution of fourth-order differential equations without reducing it to a system of first-order equations. The method of collo...
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2008-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2008/364021 |
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| _version_ | 1832553373406068736 |
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| author | S. J. Kayode |
| author_facet | S. J. Kayode |
| author_sort | S. J. Kayode |
| collection | DOAJ |
| description | The purpose of this paper is to produce an efficient zero-stable numerical
method with the same order of accuracy as that of the main starting values (predictors) for direct solution of fourth-order differential equations without reducing it to a system of first-order equations. The method of collocation of the differential system arising from the approximate solution to the problem is adopted using the power series as a basis function. The method is consistent, symmetric, and of optimal order 𝑝=6.
The main predictor for the method is also consistent, symmetric, zero-stable, and of optimal order 𝑝=6. |
| format | Article |
| id | doaj-art-ffe4936de8d04b8c92bd200cbf7e17e5 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2008-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-ffe4936de8d04b8c92bd200cbf7e17e52025-02-03T05:54:21ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252008-01-01200810.1155/2008/364021364021An Efficient Zero-Stable Numerical Method for Fourth-Order Differential EquationsS. J. Kayode0Department of Mathematical Sciences, School of Sciences, Federal University of Technology, PMB 704, Akure, Ondo State, NigeriaThe purpose of this paper is to produce an efficient zero-stable numerical method with the same order of accuracy as that of the main starting values (predictors) for direct solution of fourth-order differential equations without reducing it to a system of first-order equations. The method of collocation of the differential system arising from the approximate solution to the problem is adopted using the power series as a basis function. The method is consistent, symmetric, and of optimal order 𝑝=6. The main predictor for the method is also consistent, symmetric, zero-stable, and of optimal order 𝑝=6.http://dx.doi.org/10.1155/2008/364021 |
| spellingShingle | S. J. Kayode An Efficient Zero-Stable Numerical Method for Fourth-Order Differential Equations International Journal of Mathematics and Mathematical Sciences |
| title | An Efficient Zero-Stable Numerical Method for
Fourth-Order Differential Equations |
| title_full | An Efficient Zero-Stable Numerical Method for
Fourth-Order Differential Equations |
| title_fullStr | An Efficient Zero-Stable Numerical Method for
Fourth-Order Differential Equations |
| title_full_unstemmed | An Efficient Zero-Stable Numerical Method for
Fourth-Order Differential Equations |
| title_short | An Efficient Zero-Stable Numerical Method for
Fourth-Order Differential Equations |
| title_sort | efficient zero stable numerical method for fourth order differential equations |
| url | http://dx.doi.org/10.1155/2008/364021 |
| work_keys_str_mv | AT sjkayode anefficientzerostablenumericalmethodforfourthorderdifferentialequations AT sjkayode efficientzerostablenumericalmethodforfourthorderdifferentialequations |