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

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:235

Article

Pedas, Arvet¹  Tamme, Enn¹ 

[1] Univ Tartu, Inst Math, EE-50409 Tartu, Estonia

关键词: Fractional differential equation;    Caputo derivative;    Volterra integral equation;    Spline collocation method;    Graded grid;    Convergence analysis;   

DOI  :  10.1016/j.cam.2010.10.054

来源: Elsevier

【 摘 要 】

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. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

Free