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A non-polynomial collocation method for fractional terminal value problems

Morgado, M. Luísa; Rebelo, Magda; N. J. Ford

Proceedings of International Conference of Numerical Analysis and Applied Mathematics (ICNAAM 2012), 19–25 September 2012, Kos, Greece , 1479 (2012), 254-257

In this work we are concerned with the numerical approximation of terminal (or boundary) value problems for fractional differential equations. The approach used is based on the equivalence between this kind of problem and a Fredholm integral equation. Taking into account the potential non-smoothness of the solution of such problems at the origin, we propose a non-polynomial collocation method on a uniform mesh. Some numerical results are presented and we discuss briefly the convergence of the method.