A 2nd-order one-point numerical integration scheme for fractional ordinary differential equations
dc.contributor.author | Li, W. | |
dc.contributor.author | Wang, Shaobin | |
dc.contributor.author | Rehbock, Volker | |
dc.date.accessioned | 2017-08-24T02:21:44Z | |
dc.date.available | 2017-08-24T02:21:44Z | |
dc.date.created | 2017-08-23T07:21:28Z | |
dc.date.issued | 2017 | |
dc.identifier.citation | Li, W. and Wang, S. and Rehbock, V. 2017. A 2nd-order one-point numerical integration scheme for fractional ordinary differential equations. Numerical Algebra, Control and Optimization. 7 (3): pp. 273-287. | |
dc.identifier.uri | http://hdl.handle.net/20.500.11937/56012 | |
dc.identifier.doi | 10.3934/naco.2017018 | |
dc.description.abstract |
© 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. | |
dc.publisher | American Institute of Mathematical Sciences | |
dc.title | A 2nd-order one-point numerical integration scheme for fractional ordinary differential equations | |
dc.type | Journal Article | |
dcterms.source.volume | 7 | |
dcterms.source.number | 3 | |
dcterms.source.startPage | 273 | |
dcterms.source.endPage | 287 | |
dcterms.source.issn | 2155-3289 | |
dcterms.source.title | Numerical Algebra, Control and Optimization | |
curtin.department | Department of Chemical Engineering | |
curtin.accessStatus | Open access via publisher |
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