A Family of Modified Even Order Bernoulli-Type Multiquadric Quasi-Interpolants with Any Degree Polynomial Reproduction Property
By using the polynomial expansion in the even order Bernoulli polynomials and using the linear combinations of the shifts of the function f(x)(x∈ℝ) to approximate the derivatives of f(x), we propose a family of modified even order Bernoulli-type multiquadric quasi-interpolants which do not require t...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/389215 |
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| author | Ruifeng Wu Huilai Li Tieru Wu |
| author_facet | Ruifeng Wu Huilai Li Tieru Wu |
| author_sort | Ruifeng Wu |
| collection | DOAJ |
| description | By using the polynomial expansion in the even order Bernoulli polynomials and using the linear combinations of the
shifts of the function f(x)(x∈ℝ) to approximate the derivatives of f(x), we propose a family of modified even order Bernoulli-type multiquadric quasi-interpolants which do not require the derivatives of the function approximated at each node and can satisfy any degree polynomial reproduction property. Error estimate indicates that our operators could provide the desired precision by choosing a suitable shape-preserving parameter c and a nonnegative integer m. Numerical comparisons show that this technique provides a higher degree of accuracy. Finally, applying our operators to the fitting of discrete solutions of initial value problems, we find that our method has smaller errors than the Runge-Kutta method of order 4 and Wang et al.’s quasi-interpolation scheme. |
| format | Article |
| id | doaj-art-25304a8099174df5a018ba51b0502635 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-25304a8099174df5a018ba51b05026352025-02-03T01:01:48ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/389215389215A Family of Modified Even Order Bernoulli-Type Multiquadric Quasi-Interpolants with Any Degree Polynomial Reproduction PropertyRuifeng Wu0Huilai Li1Tieru Wu2School of Mathematics, Jilin University, Changchun 130012, ChinaSchool of Mathematics, Jilin University, Changchun 130012, ChinaSchool of Mathematics, Jilin University, Changchun 130012, ChinaBy using the polynomial expansion in the even order Bernoulli polynomials and using the linear combinations of the shifts of the function f(x)(x∈ℝ) to approximate the derivatives of f(x), we propose a family of modified even order Bernoulli-type multiquadric quasi-interpolants which do not require the derivatives of the function approximated at each node and can satisfy any degree polynomial reproduction property. Error estimate indicates that our operators could provide the desired precision by choosing a suitable shape-preserving parameter c and a nonnegative integer m. Numerical comparisons show that this technique provides a higher degree of accuracy. Finally, applying our operators to the fitting of discrete solutions of initial value problems, we find that our method has smaller errors than the Runge-Kutta method of order 4 and Wang et al.’s quasi-interpolation scheme.http://dx.doi.org/10.1155/2014/389215 |
| spellingShingle | Ruifeng Wu Huilai Li Tieru Wu A Family of Modified Even Order Bernoulli-Type Multiquadric Quasi-Interpolants with Any Degree Polynomial Reproduction Property Journal of Applied Mathematics |
| title | A Family of Modified Even Order Bernoulli-Type Multiquadric Quasi-Interpolants with Any Degree Polynomial Reproduction Property |
| title_full | A Family of Modified Even Order Bernoulli-Type Multiquadric Quasi-Interpolants with Any Degree Polynomial Reproduction Property |
| title_fullStr | A Family of Modified Even Order Bernoulli-Type Multiquadric Quasi-Interpolants with Any Degree Polynomial Reproduction Property |
| title_full_unstemmed | A Family of Modified Even Order Bernoulli-Type Multiquadric Quasi-Interpolants with Any Degree Polynomial Reproduction Property |
| title_short | A Family of Modified Even Order Bernoulli-Type Multiquadric Quasi-Interpolants with Any Degree Polynomial Reproduction Property |
| title_sort | family of modified even order bernoulli type multiquadric quasi interpolants with any degree polynomial reproduction property |
| url | http://dx.doi.org/10.1155/2014/389215 |
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