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

Authors:
Arvet Pedas;Enn Tamme
Affiliations:
-;-
Venue:
Journal of Computational and Applied Mathematics
Year:
2011

Citing 6
Cited 4

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The numerical solution of linear multi-term fractional differential equations: systems of equations

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Discrete Galerkin method for Fredholm integro-differential equations with weakly singular kernels

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Systems-based decomposition schemes for the approximate solution of multi-term fractional differential equations

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A Chebyshev spectral method based on operational matrix for initial and boundary value problems of fractional order

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Piecewise polynomial collocation for linear boundary value problems of fractional differential equations

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Waveform relaxation methods for fractional differential equations with the Caputo derivatives

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Numerical solution of nonlinear fractional differential equations by spline collocation methods

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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.