On the convergence of spline collocation methods for solving fractional differential equations

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Abstract

In the first part of this paper we study the regularity properties of solutions of initial value problems of linear multi-term fractional differential equations. We then use these results in the convergence analysis of a polynomial spline collocation method for solving such problems numerically. Using an integral equation reformulation and special non-uniform grids, global convergence estimates are derived. From these estimates it follows that the method has a rapid convergence if we use suitable nonuniform grids and the nodes of the composite Gaussian quadrature formulas as collocation points. Theoretical results are verified by some numerical examples. © 2011 Elsevier B.V. All rights reserved.

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Pedas, A., & Tamme, E. (2011). On the convergence of spline collocation methods for solving fractional differential equations. Journal of Computational and Applied Mathematics, 235(12), 3502–3514. https://doi.org/10.1016/j.cam.2010.10.054

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