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Journal of Scientific Computing

, Volume 76, Issue 1, pp 166–188 | Cite as

A Spectral Collocation Method for Nonlinear Fractional Boundary Value Problems with a Caputo Derivative

  • Chuanli Wang
  • Zhongqing WangEmail author
  • Lilian Wang
Article

Abstract

In this paper, we consider the nonlinear boundary value problems involving the Caputo fractional derivatives of order \(\alpha \in (1,2)\) on the interval (0, T). We present a Legendre spectral collocation method for the Caputo fractional boundary value problems. We derive the error bounds of the Legendre collocation method under the \(L^2\)- and \(L^\infty \)-norms. Numerical experiments are included to illustrate the theoretical results.

Keywords

Spectral collocation method Caputo fractional derivative Fredholm integral equations Convergence analysis 

Mathematics Subject Classification

65N35 45D05 41A05 41A10 41A25 

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Copyright information

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Authors and Affiliations

  1. 1.College of ScienceUniversity of Shanghai for Science and TechnologyShanghaiChina
  2. 2.School of Mathematics and StatisticsHenan University of Science and TechnologyLuo YangChina
  3. 3.School of Physical and Mathematical SciencesNanyang Technological UniversitySingaporeSingapore

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