Smoothing transformation and spline collocation for linear fractional boundary value problems

Marek Kolk, Arvet Pedas and Enn Tamme

Applied Mathematics and Computation, 2016, vol. 283, issue C, 234-250

Abstract: We construct and justify a high order method for the numerical solution of multi-point boundary value problems for linear multi-term fractional differential equations involving Caputo-type fractional derivatives. Using an integral equation reformulation of the boundary value problem we first regularize the solution by a suitable smoothing transformation. After that we solve the transformed equation by a piecewise polynomial collocation method on a mildly graded or uniform grid. Optimal global convergence estimates are derived and a superconvergence result for a special choice of collocation parameters is established. To illustrate the reliability of the proposed method some numerical results are given.

Keywords: Fractional boundary value problem; Caputo derivative; Weakly singular integral equation; Smoothing transformation; Spline collocation method (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:283:y:2016:i:c:p:234-250

DOI: 10.1016/j.amc.2016.02.044

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