DOI QR코드

DOI QR Code

SPECTRAL-COLLOCATION METHOD FOR FRACTIONAL FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS

  • Yang, Yin ;
  • Chen, Yanping ;
  • Huang, Yunqing
  • 투고 : 2013.05.20
  • 발행 : 2014.01.01

초록

We propose and analyze a spectral Jacobi-collocation approximation for fractional order integro-differential equations of Fredholm-Volterra type. The fractional derivative is described in the Caputo sense. We provide a rigorous error analysis for the collection method, which shows 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.

키워드

spectral Jacobi-collocation method;fractional order Fredholm integro-differential equations;Caputo derivative

참고문헌

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피인용 문헌

  1. Spectral-Collocation Method for Volterra Delay Integro-Differential Equations with Weakly Singular Kernels vol.8, pp.04, 2016, https://doi.org/10.4208/aamm.2015.m1088
  2. Spectral Collocation Methods for Nonlinear Volterra Integro-Differential Equations with Weakly Singular Kernels 2017, https://doi.org/10.1007/s40840-017-0487-7
  3. New Solutions for System of Fractional Integro-Differential Equations and Abel’s Integral Equations by Chebyshev Spectral Method vol.2017, 2017, https://doi.org/10.1155/2017/7853839
  4. 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
  5. Numerical Solution of Euler-Lagrange Equation with Caputo Derivatives vol.9, pp.01, 2017, https://doi.org/10.4208/aamm.2015.m970
  6. Numerical Solution of Fractional Integro-Differential Equations by Least Squares Method and Shifted Chebyshev Polynomial vol.2014, 2014, https://doi.org/10.1155/2014/431965
  7. 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
  8. Numerical simulation of time fractional Cable equations and convergence analysis vol.34, pp.5, 2017, https://doi.org/10.1002/num.22225
  9. A Numerical Method for Solving a Class of Nonlinear Second Order Fractional Volterra Integro-Differntial Type of Singularly Perturbed Problems vol.6, pp.4, 2018, https://doi.org/10.3390/math6040048

과제정보

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