A 2nd-order one-point numerical integration scheme for fractional ordinary differential equations
© 2017 Federacion Argentina de Cardiologia. All right reserved. In this paper we propose an e?cient and easy-to-implement nu-merical method for an a-th order Ordinary Differential Equation (ODE) when a ? (0, 1), based on a one-point quadrature rule. The quadrature point in each sub-interval of a giv...
| Main Authors: | , , |
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| Format: | Journal Article |
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American Institute of Mathematical Sciences
2017
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| Online Access: | http://hdl.handle.net/20.500.11937/56012 |
| _version_ | 1848759763846823936 |
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| author | Li, W. Wang, Shaobin Rehbock, Volker |
| author_facet | Li, W. Wang, Shaobin Rehbock, Volker |
| author_sort | Li, W. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | © 2017 Federacion Argentina de Cardiologia. All right reserved. In this paper we propose an e?cient and easy-to-implement nu-merical method for an a-th order Ordinary Differential Equation (ODE) when a ? (0, 1), based on a one-point quadrature rule. The quadrature point in each sub-interval of a given partition with mesh size h is chosen judiciously so that the degree of accuracy of the quadrature rule is 2 in the presence of the singu-lar integral kernel. The resulting time-stepping method can be regarded as the counterpart for fractional ODEs of the well-known mid-point method for 1st-order ODEs. We show that the global error in a numerical solution generated by this method is of the order O(h 2 ), independently of a. Numerical results are presented to demonstrate that the computed rates of convergence match the theoretical one very well and that our method is much more accurate than a well-known one-step method when a is small. |
| first_indexed | 2025-11-14T10:05:03Z |
| format | Journal Article |
| id | curtin-20.500.11937-56012 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T10:05:03Z |
| publishDate | 2017 |
| publisher | American Institute of Mathematical Sciences |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-560122017-09-13T16:10:29Z A 2nd-order one-point numerical integration scheme for fractional ordinary differential equations Li, W. Wang, Shaobin Rehbock, Volker © 2017 Federacion Argentina de Cardiologia. All right reserved. In this paper we propose an e?cient and easy-to-implement nu-merical method for an a-th order Ordinary Differential Equation (ODE) when a ? (0, 1), based on a one-point quadrature rule. The quadrature point in each sub-interval of a given partition with mesh size h is chosen judiciously so that the degree of accuracy of the quadrature rule is 2 in the presence of the singu-lar integral kernel. The resulting time-stepping method can be regarded as the counterpart for fractional ODEs of the well-known mid-point method for 1st-order ODEs. We show that the global error in a numerical solution generated by this method is of the order O(h 2 ), independently of a. Numerical results are presented to demonstrate that the computed rates of convergence match the theoretical one very well and that our method is much more accurate than a well-known one-step method when a is small. 2017 Journal Article http://hdl.handle.net/20.500.11937/56012 10.3934/naco.2017018 American Institute of Mathematical Sciences unknown |
| spellingShingle | Li, W. Wang, Shaobin Rehbock, Volker A 2nd-order one-point numerical integration scheme for fractional ordinary differential equations |
| title | A 2nd-order one-point numerical integration scheme for fractional ordinary differential equations |
| title_full | A 2nd-order one-point numerical integration scheme for fractional ordinary differential equations |
| title_fullStr | A 2nd-order one-point numerical integration scheme for fractional ordinary differential equations |
| title_full_unstemmed | A 2nd-order one-point numerical integration scheme for fractional ordinary differential equations |
| title_short | A 2nd-order one-point numerical integration scheme for fractional ordinary differential equations |
| title_sort | 2nd-order one-point numerical integration scheme for fractional ordinary differential equations |
| url | http://hdl.handle.net/20.500.11937/56012 |