Fast Numerical Contour Integral Method for Fractional Diffusion Equations
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[1] Paolo Tilli. Singular values and eigenvalues of non-hermitian block Toeplitz matrices , 1996 .
[2] Siu-Long Lei,et al. Circulant and skew-circulant splitting iteration for fractional advection–diffusion equations , 2014, Int. J. Comput. Math..
[3] I. Podlubny. Fractional differential equations , 1998 .
[4] J. Kirchner,et al. Fractal stream chemistry and its implications for contaminant transport in catchments , 2000, Nature.
[5] Hyoseop Lee,et al. Laplace Transform Method for Parabolic Problems with Time-Dependent Coefficients , 2013, SIAM J. Numer. Anal..
[6] X. Li,et al. Existence and Uniqueness of the Weak Solution of the Space-Time Fractional Diffusion Equation and a Spectral Method Approximation , 2010 .
[7] M. Meerschaert,et al. Finite difference approximations for two-sided space-fractional partial differential equations , 2006 .
[8] Enrico Scalas,et al. Waiting-times and returns in high-frequency financial data: an empirical study , 2002, cond-mat/0203596.
[9] Dongwoo Sheen,et al. A parallel method for time discretization of parabolic equations based on Laplace transformation and quadrature , 2003 .
[10] M. Meerschaert,et al. Finite difference approximations for fractional advection-dispersion flow equations , 2004 .
[11] Vidar Thomée,et al. Time discretization via Laplace transformation of an integro-differential equation of parabolic type , 2006, Numerische Mathematik.
[12] V. Thomée,et al. Maximum-norm error analysis of a numerical solution via Laplace transformation and quadrature of a fractional-order evolution equation , 2010 .
[13] Raymond H. Chan,et al. An Introduction to Iterative Toeplitz Solvers (Fundamentals of Algorithms) , 2007 .
[14] D. Benson,et al. Fractional Dispersion, Lévy Motion, and the MADE Tracer Tests , 2001 .
[15] K. J. in 't Hout,et al. A Contour Integral Method for the Black-Scholes and Heston Equations , 2009, SIAM J. Sci. Comput..
[16] Ivan P. Gavrilyuk,et al. Exponentially Convergent Algorithms for the Operator Exponential with Applications to Inhomogeneous Problems in Banach Spaces , 2005, SIAM J. Numer. Anal..
[17] R. Tyrrell Rockafellar,et al. Convex Analysis , 1970, Princeton Landmarks in Mathematics and Physics.
[18] C. Palencia,et al. On the numerical inversion of the Laplace transform of certain holomorphic mappings , 2004 .
[19] A. Talbot. The Accurate Numerical Inversion of Laplace Transforms , 1979 .
[20] Charles R. Johnson,et al. Topics in Matrix Analysis , 1991 .
[21] Hai-Wei Sun,et al. Multigrid method for fractional diffusion equations , 2012, J. Comput. Phys..
[22] V. Thomée,et al. Time discretization of an evolution equation via Laplace transforms , 2004 .
[23] Hai-Wei Sun,et al. Shift-Invert Arnoldi Approximation to the Toeplitz Matrix Exponential , 2010, SIAM J. Sci. Comput..
[24] Michael K. Ng,et al. Preconditioning Techniques for Diagonal-times-Toeplitz Matrices in Fractional Diffusion Equations , 2014, SIAM J. Sci. Comput..
[25] Dongwoo Sheen,et al. A parallel method for time-discretization of parabolic problems based on contour integral representation and quadrature , 2000, Math. Comput..
[26] Han Zhou,et al. Quasi-Compact Finite Difference Schemes for Space Fractional Diffusion Equations , 2012, J. Sci. Comput..
[27] R. Hilfer. Applications Of Fractional Calculus In Physics , 2000 .
[28] Xiao-Qing Jin,et al. Preconditioned iterative methods for fractional diffusion equation , 2014, J. Comput. Phys..
[29] Hong Wang,et al. An O(N log2N) alternating-direction finite difference method for two-dimensional fractional diffusion equations , 2011, J. Comput. Phys..
[30] Hong Wang,et al. A Fast Finite Difference Method for Two-Dimensional Space-Fractional Diffusion Equations , 2012, SIAM J. Sci. Comput..
[31] Fawang Liu,et al. Numerical solution of the space fractional Fokker-Planck equation , 2004 .
[32] Hong Wang,et al. A direct O(N log2 N) finite difference method for fractional diffusion equations , 2010, J. Comput. Phys..
[33] Mark M. Meerschaert,et al. A second-order accurate numerical method for the two-dimensional fractional diffusion equation , 2007, J. Comput. Phys..
[34] V. Thomée,et al. Numerical solution via Laplace transforms of a fractional order evolution equation , 2010 .
[35] R. Chan,et al. An Introduction to Iterative Toeplitz Solvers , 2007 .
[36] Mark M. Meerschaert,et al. A second-order accurate numerical approximation for the fractional diffusion equation , 2006, J. Comput. Phys..
[37] Fawang Liu,et al. Error analysis of an explicit finite difference approximation for the space fractional diffusion equation with insulated ends , 2005 .
[38] R. Magin. Fractional Calculus in Bioengineering , 2006 .
[39] M. N. Spijker. Numerical ranges and stability estimates , 1993 .
[40] J. A. C. Weideman,et al. Improved contour integral methods for parabolic PDEs , 2010 .
[41] Cesar Palencia,et al. A spectral order method for inverting sectorial Laplace transforms , 2005 .
[42] Richard L Magin,et al. Fractional calculus in bioengineering, part 2. , 2004, Critical reviews in biomedical engineering.
[43] Lloyd N. Trefethen,et al. Parabolic and hyperbolic contours for computing the Bromwich integral , 2007, Math. Comput..
[44] Siu-Long Lei,et al. A circulant preconditioner for fractional diffusion equations , 2013, J. Comput. Phys..