Volume 48, pp. 387-406, 2018.

High-order Legendre collocation method for fractional-order linear semi-explicit differential algebraic equations

F. Ghanbari, K. Ghanbari, and P. Mokhtary

Abstract

This paper is devoted to a high-order Legendre collocation approximation for solving fractional-order linear semi-explicit differential algebraic equations numerically. We discuss existence, uniqueness, and regularity results and conclude that the solutions typically suffer from a singularity at the origin. Moreover, we show that the representation of the approximate solutions by a linear combination of Legendre polynomials leads to unsatisfactory convergence results. To overcome this difficulty, we develop a new regularization approach that removes the singularity of the input data and produces approximate solutions of higher accuracy. Illustrative numerical examples are presented to support the obtained theoretical results.

Full Text (PDF) [346 KB]

Key words

fractional-order differential algebraic equation, Legendre collocation method, regularization approach.

AMS subject classifications

34A08, 65L05, 65L20, 65L60, 65L80.

Links to the cited ETNA articles

[10]Vol. 41 (2014), pp. 289-305 P. Mokhtary and F. Ghoreishi: Convergence analysis of the operational Tau method for Abel-type Volterra integral equations

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