Spectral Collocation Methods for Nonlinear Volterra Integro-Differential Equations with Weakly Singular Kernels

  • Yin YangEmail author
  • Yanping Chen


A spectral Jacobi-collocation approximation is proposed and analyzed for nonlinear integro-differential equations of Volterra type with weakly singular kernel, and a rigorous error analysis is provided for the spectral methods to show both the errors of approximate solutions and the errors of approximate derivatives of the solutions decaying exponentially in infinity-norm and weighted \(L^2\)-norm. Numerical results are presented to confirm the theoretical prediction of the exponential rate of convergence.


Spectral collocation method Nonlinear Volterra integro-differential equations 



The work was supported by NSFC Project (11671342, 91430213, 11671157), and Hunan Province Natural Science Fund (2016JJ3114).


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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2017

Authors and Affiliations

  1. 1.School of Mathematics and Computational ScienceXiangtan UniversityXiangtanPeople’s Republic of China
  2. 2.School of Mathematical SciencesSouth China Normal UniversityGuangzhouPeople’s Republic of China

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