An Exponential Spline Difference Scheme for Solving a Class of Boundary Value Problems of Second-Order Ordinary Differential Equations
In this paper, we mainly study an exponential spline function space, construct a basis with local supports, and present the relationship between the function value and the first and the second derivative at the nodes. Using these relations, we construct an exponential spline-based difference scheme...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2020/7056254 |
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| _version_ | 1832547052121227264 |
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| author | Dunqian Cao |
| author_facet | Dunqian Cao |
| author_sort | Dunqian Cao |
| collection | DOAJ |
| description | In this paper, we mainly study an exponential spline function space, construct a basis with local supports, and present the relationship between the function value and the first and the second derivative at the nodes. Using these relations, we construct an exponential spline-based difference scheme for solving a class of boundary value problems of second-order ordinary differential equations (ODEs) and analyze the error and the convergence of this method. The results show that the algorithm is high accurate and conditionally convergent, and an accuracy of 1/240h6 was achieved with smooth functions. |
| format | Article |
| id | doaj-art-f05530b3d60d444196dbdcefd9256178 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-f05530b3d60d444196dbdcefd92561782025-02-03T06:46:19ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2020-01-01202010.1155/2020/70562547056254An Exponential Spline Difference Scheme for Solving a Class of Boundary Value Problems of Second-Order Ordinary Differential EquationsDunqian Cao0School of Mathematics and Physics, Guangxi University for Nationalities, Nanning 530006, ChinaIn this paper, we mainly study an exponential spline function space, construct a basis with local supports, and present the relationship between the function value and the first and the second derivative at the nodes. Using these relations, we construct an exponential spline-based difference scheme for solving a class of boundary value problems of second-order ordinary differential equations (ODEs) and analyze the error and the convergence of this method. The results show that the algorithm is high accurate and conditionally convergent, and an accuracy of 1/240h6 was achieved with smooth functions.http://dx.doi.org/10.1155/2020/7056254 |
| spellingShingle | Dunqian Cao An Exponential Spline Difference Scheme for Solving a Class of Boundary Value Problems of Second-Order Ordinary Differential Equations Discrete Dynamics in Nature and Society |
| title | An Exponential Spline Difference Scheme for Solving a Class of Boundary Value Problems of Second-Order Ordinary Differential Equations |
| title_full | An Exponential Spline Difference Scheme for Solving a Class of Boundary Value Problems of Second-Order Ordinary Differential Equations |
| title_fullStr | An Exponential Spline Difference Scheme for Solving a Class of Boundary Value Problems of Second-Order Ordinary Differential Equations |
| title_full_unstemmed | An Exponential Spline Difference Scheme for Solving a Class of Boundary Value Problems of Second-Order Ordinary Differential Equations |
| title_short | An Exponential Spline Difference Scheme for Solving a Class of Boundary Value Problems of Second-Order Ordinary Differential Equations |
| title_sort | exponential spline difference scheme for solving a class of boundary value problems of second order ordinary differential equations |
| url | http://dx.doi.org/10.1155/2020/7056254 |
| work_keys_str_mv | AT dunqiancao anexponentialsplinedifferenceschemeforsolvingaclassofboundaryvalueproblemsofsecondorderordinarydifferentialequations AT dunqiancao exponentialsplinedifferenceschemeforsolvingaclassofboundaryvalueproblemsofsecondorderordinarydifferentialequations |