Local Polynomial Regression Solution for Partial Differential Equations with Initial and Boundary Values
Local polynomial regression (LPR) is applied to solve the partial differential equations (PDEs). Usually, the solutions of the problems are separation of variables and eigenfunction expansion methods, so we are rarely able to find analytical solutions. Consequently, we must try to find numerical sol...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2012/201678 |
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| _version_ | 1850217036071829504 |
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| author | Liyun Su Tianshun Yan Yanyong Zhao Fenglan Li |
| author_facet | Liyun Su Tianshun Yan Yanyong Zhao Fenglan Li |
| author_sort | Liyun Su |
| collection | DOAJ |
| description | Local polynomial regression (LPR) is applied to solve the partial differential equations (PDEs). Usually, the solutions of the problems are
separation of variables and eigenfunction expansion methods, so we are rarely
able to find analytical solutions. Consequently, we must try to find numerical
solutions. In this paper, two test problems are considered for the numerical
illustration of the method. Comparisons are made between the exact solutions and the results of the LPR. The results of applying this theory to the
PDEs reveal that LPR method possesses very high accuracy, adaptability,
and efficiency; more importantly, numerical illustrations indicate that the new
method is much more efficient than B-splines and AGE methods derived for
the same purpose. |
| format | Article |
| id | doaj-art-2facb6abc0ae4f449dbf5c89d9872ebf |
| institution | OA Journals |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-2facb6abc0ae4f449dbf5c89d9872ebf2025-08-20T02:08:10ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2012-01-01201210.1155/2012/201678201678Local Polynomial Regression Solution for Partial Differential Equations with Initial and Boundary ValuesLiyun Su0Tianshun Yan1Yanyong Zhao2Fenglan Li3School of Mathematics and Statistics, Chongqing University of Technology, Chongqing 400054, ChinaSchool of Mathematics and Statistics, Chongqing University of Technology, Chongqing 400054, ChinaSchool of Mathematics and Statistics, Chongqing University of Technology, Chongqing 400054, ChinaInstitute of Library, Chongqing University of Technology, Chongqing 400054, ChinaLocal polynomial regression (LPR) is applied to solve the partial differential equations (PDEs). Usually, the solutions of the problems are separation of variables and eigenfunction expansion methods, so we are rarely able to find analytical solutions. Consequently, we must try to find numerical solutions. In this paper, two test problems are considered for the numerical illustration of the method. Comparisons are made between the exact solutions and the results of the LPR. The results of applying this theory to the PDEs reveal that LPR method possesses very high accuracy, adaptability, and efficiency; more importantly, numerical illustrations indicate that the new method is much more efficient than B-splines and AGE methods derived for the same purpose.http://dx.doi.org/10.1155/2012/201678 |
| spellingShingle | Liyun Su Tianshun Yan Yanyong Zhao Fenglan Li Local Polynomial Regression Solution for Partial Differential Equations with Initial and Boundary Values Discrete Dynamics in Nature and Society |
| title | Local Polynomial Regression Solution for Partial Differential Equations with Initial and Boundary Values |
| title_full | Local Polynomial Regression Solution for Partial Differential Equations with Initial and Boundary Values |
| title_fullStr | Local Polynomial Regression Solution for Partial Differential Equations with Initial and Boundary Values |
| title_full_unstemmed | Local Polynomial Regression Solution for Partial Differential Equations with Initial and Boundary Values |
| title_short | Local Polynomial Regression Solution for Partial Differential Equations with Initial and Boundary Values |
| title_sort | local polynomial regression solution for partial differential equations with initial and boundary values |
| url | http://dx.doi.org/10.1155/2012/201678 |
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