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math.NA2018★ 5 cited
Stochastic Solution of Elliptic and Parabolic Boundary Value Problems for the Spectral Fractional Laplacian
Mamikon Gulian, Guofei Pang
We prove and implement stochastic solution (or Feynman-Kac) formulas for boundary value problems involving the spectral fractional Laplacian with nonzero Dirichlet boundary conditi…
math.NA2018★ 2 cited
Radial basis function collocation method for decoupled fractional Laplacian wave equations
Yiran Xu, Jingye Li, Guofei Pang +2
Decoupled fractional Laplacian wave equation can describe the seismic wave propagation in attenuating media. Fourier pseudospectral implementations, which solve the equation in spa…
math.NA2018★ 65 cited
What Is the Fractional Laplacian?
Anna Lischke, Guofei Pang, Mamikon Gulian +8
The fractional Laplacian in R^d has multiple equivalent characterizations. Moreover, in bounded domains, boundary conditions must be incorporated in these characterizations in math…