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

Authors:
Arvet Pedas;Enn Tamme
Affiliations:
-;-
Venue:
Journal of Computational and Applied Mathematics
Year:
2012

Citing 9
Cited 2

Piecewise Polynomial Collocation Methods for Linear Volterra Integro-Differential Equations with Weakly Singular Kernels

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

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Spline collocation method for 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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On some explicit Adams multistep methods for fractional differential equations

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

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Existence theory for anti-periodic boundary value problems of fractional differential equations and inclusions

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Some boundary value problems of fractional differential equations and inclusions

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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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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

We consider a class of boundary value problems for linear multi-term fractional differential equations which involve Caputo-type fractional derivatives. Using an integral equation reformulation of the boundary value problem, some regularity properties of the exact solution are derived. Based on these properties, the numerical solution of boundary value problems by piecewise polynomial collocation methods is discussed. In particular, we study the attainable order of convergence of proposed algorithms and show how the convergence rate depends on the choice of the grid and collocation points. Theoretical results are verified by two numerical examples.