In this paper, we develop an accurate collocation scheme for ordinary initial value problems of the Caputo type and in order to illustrate the performance of the method we provide several numerical examples. At the end, we also indicate how this method can be used to approximate the solution of time-fractional diffusion equations. At it will be seen, it allows us to obtain accurate solutions even when the solution is not smooth at the origin.
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The authors acknowledge the Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) through projects MULTI/04621/2019 and UIDB/00297/2020 (Centro de Matemática e Aplicações), respectively.
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Morgado, M.L., Rebelo, M. (2020). Collocation Solution of Fractional Differential Equations in Piecewise Nonpolynomial Spaces. In: Pinelas, S., Graef, J.R., Hilger, S., Kloeden, P., Schinas, C. (eds) Differential and Difference Equations with Applications. ICDDEA 2019. Springer Proceedings in Mathematics & Statistics, vol 333. Springer, Cham. https://doi.org/10.1007/978-3-030-56323-3_36
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-56322-6
Online ISBN: 978-3-030-56323-3