A Spectral Method (of Exponential Convergence) for Singular Solutions of the Diffusion Equation with General Two-Sided Fractional Derivative

@article{Mao2018ASM,
  title={A Spectral Method (of Exponential Convergence) for Singular Solutions of the Diffusion Equation with General Two-Sided Fractional Derivative},
  author={Zhiping Mao and George Em Karniadakis},
  journal={SIAM J. Numerical Analysis},
  year={2018},
  volume={56},
  pages={24-49}
}
An open problem in the numerical solution of fractional partial differential equations (FPDEs) is how to obtain high-order accuracy for singular solutions; even for smooth right-hand sides solutions of FPDEs are singular. Here, we consider the one-dimensional diffusion equation with general two-sided fractional derivative characterized by a parameter p ∈ [0, 1]; for p = 1/2 we recover the Riesz fractional derivative, while for p = 1, 0 we obtain the one-sided fractional derivative. We employ a… CONTINUE READING

References

Publications referenced by this paper.
Showing 1-10 of 28 references

Survey lectures on the mathematical foundations of the finite element method

  • I. Babuška, A. K. Aziz
  • The Mathematical Foundations of the Finite…
  • 1972
Highly Influential
3 Excerpts

Adaptive finite element method for fractional differential equations using hierarchical matrices

  • X. Zhao, X. Hu, W. Cai, G. E. Karniadakis
  • Comput. Methods Appl. Mech. Engrg., 325
  • 2017
1 Excerpt

– Galerkin finite element method for fractional convection - diffusion equations

  • Z. Zhou, A Petrov
  • SIAM J . Numer . Anal .
  • 2016

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