A 2nd-order one-point numerical integration scheme for fractional ordinary differential equations
|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.|
© 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|
|dcterms.source.title||Numerical Algebra, Control and Optimization|
|curtin.department||Department of Chemical Engineering|
|curtin.accessStatus||Open access via publisher|
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