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DOI QR Code

JACOBI SPECTRAL GALERKIN METHODS FOR VOLTERRA INTEGRAL EQUATIONS WITH WEAKLY SINGULAR KERNEL

  • Yang, Yin
  • Received : 2015.02.01
  • Published : 2016.01.31

Abstract

We propose and analyze spectral and pseudo-spectral Jacobi-Galerkin approaches for weakly singular Volterra integral equations (VIEs). We provide a rigorous error analysis for spectral and pseudo-spectral Jacobi-Galerkin methods, which show that the errors of the approximate solution decay exponentially in $L^{\infty}$ norm and weighted $L^2$-norm. The numerical examples are given to illustrate the theoretical results.

Keywords

spectral Galerkin methods;Jacobi polynomial;Volterra integral equations with weakly singular kernels

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Cited by

  1. Spectral Collocation Methods for Nonlinear Volterra Integro-Differential Equations with Weakly Singular Kernels 2017, https://doi.org/10.1007/s40840-017-0487-7
  2. Numerical solutions for solving time fractional Fokker–Planck equations based on spectral collocation methods 2017, https://doi.org/10.1016/j.cam.2017.04.003
  3. Spectral collocation method for the time-fractional diffusion-wave equation and convergence analysis vol.73, pp.6, 2017, https://doi.org/10.1016/j.camwa.2016.08.017
  4. Jacobi Spectral Galerkin and Iterated Methods for Nonlinear Volterra Integral Equation vol.11, pp.4, 2016, https://doi.org/10.1115/1.4033439
  5. Numerical simulation of time fractional Cable equations and convergence analysis vol.34, pp.5, 2017, https://doi.org/10.1002/num.22225

Acknowledgement

Supported by : NSFC, Hunan Provincial Science and Technology Department