The Cardinal Spline Methods for the Numerical Solution of Nonlinear Integral Equations
In this study, an effective technique is presented for solving nonlinear Volterra integral equations. The method is based on application of cardinal spline functions on small compact supports. The integral equation is reduced to a system of algebra equations. Since the matrix for the system is trian...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Chemistry |
| Online Access: | http://dx.doi.org/10.1155/2020/3236813 |
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| _version_ | 1832560703346573312 |
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| author | Xiaoyan Liu Jin Xie Zhi Liu Jiahuan Huang |
| author_facet | Xiaoyan Liu Jin Xie Zhi Liu Jiahuan Huang |
| author_sort | Xiaoyan Liu |
| collection | DOAJ |
| description | In this study, an effective technique is presented for solving nonlinear Volterra integral equations. The method is based on application of cardinal spline functions on small compact supports. The integral equation is reduced to a system of algebra equations. Since the matrix for the system is triangular, it is relatively straightforward to solve for the unknowns and an approximation of the original solution with high accuracy is accomplished. Several cardinal splines are employed in the paper to enhance the accuracy. The sufficient condition for the existence of the inverse matrix is examined, and the convergence rate is analyzed. We compare our method with other methods proposed in recent papers and demonstrated the advantage of our method with several examples. |
| format | Article |
| id | doaj-art-e1ba32b21fea45f1baa1949befde764a |
| institution | Kabale University |
| issn | 2090-9063 2090-9071 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Chemistry |
| spelling | doaj-art-e1ba32b21fea45f1baa1949befde764a2025-02-03T01:26:57ZengWileyJournal of Chemistry2090-90632090-90712020-01-01202010.1155/2020/32368133236813The Cardinal Spline Methods for the Numerical Solution of Nonlinear Integral EquationsXiaoyan Liu0Jin Xie1Zhi Liu2Jiahuan Huang3Department of Mathematic, University of La Verne, La Verne, CA 91750, USASchool of Artificial Intelligence and Big Data, Hefei University, Hefei 230601, ChinaSchool of Mathematic, Hefei University of Technology, Hefei 230001, ChinaDepartment of Mathematic, University of La Verne, La Verne, CA 91750, USAIn this study, an effective technique is presented for solving nonlinear Volterra integral equations. The method is based on application of cardinal spline functions on small compact supports. The integral equation is reduced to a system of algebra equations. Since the matrix for the system is triangular, it is relatively straightforward to solve for the unknowns and an approximation of the original solution with high accuracy is accomplished. Several cardinal splines are employed in the paper to enhance the accuracy. The sufficient condition for the existence of the inverse matrix is examined, and the convergence rate is analyzed. We compare our method with other methods proposed in recent papers and demonstrated the advantage of our method with several examples.http://dx.doi.org/10.1155/2020/3236813 |
| spellingShingle | Xiaoyan Liu Jin Xie Zhi Liu Jiahuan Huang The Cardinal Spline Methods for the Numerical Solution of Nonlinear Integral Equations Journal of Chemistry |
| title | The Cardinal Spline Methods for the Numerical Solution of Nonlinear Integral Equations |
| title_full | The Cardinal Spline Methods for the Numerical Solution of Nonlinear Integral Equations |
| title_fullStr | The Cardinal Spline Methods for the Numerical Solution of Nonlinear Integral Equations |
| title_full_unstemmed | The Cardinal Spline Methods for the Numerical Solution of Nonlinear Integral Equations |
| title_short | The Cardinal Spline Methods for the Numerical Solution of Nonlinear Integral Equations |
| title_sort | cardinal spline methods for the numerical solution of nonlinear integral equations |
| url | http://dx.doi.org/10.1155/2020/3236813 |
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