Fast Fourier-like Mapped Chebyshev Spectral-Galerkin Methods for PDEs with Integral Fractional Laplacian in Unbounded Domains
暂无分享,去创建一个
Jie Shen | Li-Lian Wang | Tao Tang | Huifang Yuan | Changtao Sheng | Changtao Sheng | Jie Shen | T. Tang | Lilian Wang | Huifang Yuan
[1] Jie Shen,et al. Error Analysis for Mapped Legendre Spectral and Pseudospectral Methods , 2004, SIAM J. Numer. Anal..
[2] Tao Zhou,et al. Rational Spectral Methods for PDEs Involving Fractional Laplacian in Unbounded Domains , 2019, SIAM J. Sci. Comput..
[3] Chuanju Xu,et al. A fractional spectral method with applications to some singular problems , 2016, Adv. Comput. Math..
[4] Xiaochuan Tian,et al. Numerical methods for nonlocal and fractional models , 2020, Acta Numerica.
[5] Jie Shen,et al. A Fourth-Order Time-Splitting Laguerre-Hermite Pseudospectral Method for Bose-Einstein Condensates , 2005, SIAM J. Sci. Comput..
[6] Jie Shen,et al. Spectral Methods: Algorithms, Analysis and Applications , 2011 .
[7] Jie Shen,et al. Approximations by orthonormal mapped Chebyshev functions for higher-dimensional problems in unbounded domains , 2014, J. Comput. Appl. Math..
[8] E. Valdinoci,et al. Hitchhiker's guide to the fractional Sobolev spaces , 2011, 1104.4345.
[9] Yanzhi Zhang,et al. Accurate numerical methods for two and three dimensional integral fractional Laplacian with applications , 2019 .
[10] Jie Shen,et al. Hermite Spectral Methods for Fractional PDEs in Unbounded Domains , 2017, SIAM J. Sci. Comput..
[11] Timothy R. Ginn,et al. Nonlocal dispersion in media with continuously evolving scales of heterogeneity , 1993 .
[12] Bangti Jin,et al. Numerical Analysis of Nonlinear Subdiffusion Equations , 2017, SIAM J. Numer. Anal..
[13] Qiang Du,et al. Nonlocal Modeling, Analysis, and Computation , 2019 .
[14] L. Caffarelli,et al. An Extension Problem Related to the Fractional Laplacian , 2006, math/0608640.
[15] Guo Ben-yu,et al. Modified Chebyshev rational spectral method for the whole line , 2003 .
[16] Xu Guo,et al. A High Order Finite Difference Method for Tempered Fractional Diffusion Equations with Applications to the CGMY Model , 2018, SIAM J. Sci. Comput..
[17] A. Aziz. The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations , 1972 .
[18] S. N. Mahmoodi,et al. The fractional viscoelastic response of human breast tissue cells , 2015, Physical biology.
[19] H. Bateman,et al. Higher Transcendental Functions [Volumes I-III] , 1953 .
[20] Zhiping Mao,et al. Jacobi-Galerkin spectral method for eigenvalue problems of Riesz fractional differential equations , 2018, 1803.03556.
[21] Weihua Deng,et al. Time Discretization of a Tempered Fractional Feynman-Kac Equation with Measure Data , 2018, SIAM J. Numer. Anal..
[22] Ricardo H. Nochetto,et al. Numerical methods for fractional diffusion , 2017, Comput. Vis. Sci..
[23] Nicolas E. Humphries,et al. Scaling laws of marine predator search behaviour , 2008, Nature.
[24] H. Yoshida. Construction of higher order symplectic integrators , 1990 .
[25] Jie Shen,et al. Some Recent Advances on Spectral Methods for Unbounded Domains , 2008 .
[26] Yanzhi Zhang,et al. Computing the ground and first excited states of the fractional Schrodinger equation in an infinite potential well , 2014, 1405.0409.
[27] Bruce J. West,et al. Lévy dynamics of enhanced diffusion: Application to turbulence. , 1987, Physical review letters.
[28] Weihua Deng,et al. A Riesz Basis Galerkin Method for the Tempered Fractional Laplacian , 2018, SIAM J. Numer. Anal..
[29] T. MacRobert. Higher Transcendental Functions , 1955, Nature.
[30] T. Tang,et al. Hermite spectral collocation methods for fractional PDEs in unbounded domains , 2018, 1801.09073.
[31] Wei Cai,et al. What Is the Fractional Laplacian , 2018, 1801.09767.
[32] Raytcho D. Lazarov,et al. Error Estimates for a Semidiscrete Finite Element Method for Fractional Order Parabolic Equations , 2012, SIAM J. Numer. Anal..
[33] Weiwei Sun,et al. Hermite Spectral Methods with a Time-Dependent Scaling for Parabolic Equations in Unbounded Domains , 2005, SIAM J. Numer. Anal..
[34] Tsuyoshi Murata,et al. {m , 1934, ACML.
[35] Joseph E. Pasciak,et al. Numerical approximation of the integral fractional Laplacian , 2017, Numerische Mathematik.
[36] Naomichi Hatano,et al. Dispersive transport of ions in column experiments: An explanation of long‐tailed profiles , 1998 .
[37] Mark Ainsworth,et al. Aspects of an adaptive finite element method for the fractional Laplacian: A priori and a posteriori error estimates, efficient implementation and multigrid solver☆☆☆ , 2017, 1708.03912.
[38] M. Nikolenko,et al. Translated from Russian by , 2008 .
[39] Guofei Pang,et al. What is the fractional Laplacian? A comparative review with new results , 2020, J. Comput. Phys..
[40] Joseph E. Pasciak,et al. On sinc quadrature approximations of fractional powers of regularly accretive operators , 2017, J. Num. Math..
[41] Mark Ainsworth,et al. Hybrid Finite Element-Spectral Method for the Fractional Laplacian: Approximation Theory and Efficient Solver , 2018, SIAM J. Sci. Comput..
[42] Adam M. Oberman,et al. Numerical Methods for the Fractional Laplacian: A Finite Difference-Quadrature Approach , 2013, SIAM J. Numer. Anal..
[43] Jie Shen,et al. Laguerre Functions and Their Applications to Tempered Fractional Differential Equations on Infinite Intervals , 2018, J. Sci. Comput..
[44] Joseph Lipka,et al. A Table of Integrals , 2010 .
[45] Ricardo H. Nochetto,et al. A PDE Approach to Space-Time Fractional Parabolic Problems , 2014, SIAM J. Numer. Anal..
[46] Rene F. Swarttouw,et al. Orthogonal polynomials , 2020, NIST Handbook of Mathematical Functions.
[47] T. Geisel,et al. The scaling laws of human travel , 2006, Nature.
[48] Tao Tang,et al. The Hermite Spectral Method for Gaussian-Type Functions , 1993, SIAM J. Sci. Comput..
[49] S. Silling. Reformulation of Elasticity Theory for Discontinuities and Long-Range Forces , 2000 .
[50] Ricardo H. Nochetto,et al. A PDE Approach to Fractional Diffusion in General Domains: A Priori Error Analysis , 2013, Found. Comput. Math..
[51] D. Benson,et al. Application of a fractional advection‐dispersion equation , 2000 .
[52] M. Agranovich,et al. Sobolev Spaces, Their Generalizations and Elliptic Problems in Smooth and Lipschitz Domains , 2015 .
[53] Weihua Deng,et al. Finite Element Method for the Space and Time Fractional Fokker-Planck Equation , 2008, SIAM J. Numer. Anal..
[54] J. Klafter,et al. The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics , 2004 .
[55] Gabriel Acosta,et al. A Fractional Laplace Equation: Regularity of Solutions and Finite Element Approximations , 2015, SIAM J. Numer. Anal..
[56] Jie Shen,et al. Efficient and accurate spectral method using generalized Jacobi functions for solving Riesz fractional differential equations , 2016 .
[57] E. Montroll. Random walks on lattices , 1969 .
[58] J. Klafter,et al. The random walk's guide to anomalous diffusion: a fractional dynamics approach , 2000 .
[59] P. Markowich,et al. Numerical study of fractional nonlinear Schrödinger equations , 2014, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.
[60] G. Burton. Sobolev Spaces , 2013 .
[61] Gabriel Acosta,et al. A short FE implementation for a 2d homogeneous Dirichlet problem of a fractional Laplacian , 2016, Comput. Math. Appl..