대한수학회지 (Journal of the Korean Mathematical Society)

  • 제51권1호
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  • Pages.203-224
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  • 2014
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  • 0304-9914(pISSN)
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  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지
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SPECTRAL-COLLOCATION METHOD FOR FRACTIONAL FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS

  • Yang, Yin (Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University) ;
  • Chen, Yanping (School of Mathematical Sciences South China Normal University) ;
  • Huang, Yunqing (Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University)
  • 투고 : 2013.05.20
  • 발행 : 2014.01.01
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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.

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참고문헌

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  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
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  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