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A three-level finite difference method with preconditioning technique for two-dimensional nonlinear fractional complex Ginzburg–Landau equations Journal article
Journal of Computational and Applied Mathematics, 2021,Volume: 389
Authors:  Zhang,Qifeng;  Zhang,Lu;  Sun,Hai wei
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Boundedness  Circulant preconditioner  Crank–Nicolson scheme  Space fractional Ginzburg–Landau equation  
Circulant-based approximate inverse preconditioners for a class of fractional diffusion equations Journal article
Computers and Mathematics with Applications, 2021,Volume: 85,Page: 18-29
Authors:  Pang,Hong Kui;  Qin,Hai Hua;  Sun,Hai Wei;  Ma,Ting Ting
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Circulant-based preconditioner  Decay property  Finite difference method  Fractional diffusion equation  Toeplitz-like  
Fast implicit difference schemes for time-space fractional diffusion equations with the integral fractional Laplacian Journal article
Mathematical Methods in the Applied Sciences, 2021,Volume: 44,Issue: 1,Page: 441-463
Authors:  Gu,Xian Ming;  Sun,Hai Wei;  Zhang,Yanzhi;  Zhao,Yong Liang
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Caputo derivative  circulant preconditioner  fractional diffusion equations  integral fractional Laplacian  Krylov subspace solvers  
Gap probabilities in the Laguerre unitary ensemble and discrete Painlevé equations Journal article
Journal of Physics A: Mathematical and Theoretical, 2020,Volume: 53,Issue: 35
Authors:  Hu,Jie;  Dzhamay,Anton;  Chen,Yang
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birational transformations  difference equations  orthogonal polynomials  Painleve equations  
A fast method for variable-order Caputo fractional derivative with applications to time-fractional diffusion equations Journal article
Computers and Mathematics with Applications, 2020,Volume: 80,Issue: 5,Page: 1443-1458
Authors:  Fang,Zhi Wei;  Sun,Hai Wei;  Wang,Hong
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Fast and memory-saving algorithm  Shifted binary block partition  Time-fractional diffusion equations  Uniform polynomial approximation  Variable-order Caputo fractional derivative  
Orthogonal polynomials, bi-confluent Heun equations and semi-classical weights Journal article
Journal of Difference Equations and Applications, 2020,Volume: 26,Issue: 7,Page: 1000-1012
Authors:  Wang,Dan;  Zhu,Mengkun;  Chen,Yang
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asymptotic  Bi-confluent Heun equation  Orthogonal polynomials  semi-classical  
Exponential Runge–Kutta Method for Two-Dimensional Nonlinear Fractional Complex Ginzburg–Landau Equations Journal article
Journal of Scientific Computing, 2020,Volume: 83,Issue: 3
Authors:  Zhang,Lu;  Zhang,Qifeng;  Sun,Hai Wei
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Exponential Runge–Kutta method  Matrix exponential  Shift-invert Lanczos method  Space fractional Ginzburg–Landau equation  Toeplitz structure  
A nonuniform L2 formula of Caputo derivative and its application to a fractional Benjamin–Bona–Mahony-type equation with nonsmooth solutions Journal article
Numerical Methods for Partial Differential Equations, 2020,Volume: 36,Issue: 3,Page: 579-600
Authors:  Lyu,Pin;  Vong,Seakweng
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Caputo derivative  finite difference scheme  fractional BBM-type equation  nonuniform time grid  unconditional convergence  
Fast solvers for finite difference scheme of two-dimensional time-space fractional differential equations Journal article
Numerical Algorithms, 2020,Volume: 84,Issue: 1,Page: 37-62
Authors:  Huang,Yun Chi;  Lei,Siu Long
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Alternating direction implicit scheme  Block lower triangular Toeplitz matrix  Divide-and-conquer  Time-marching  Time-space fractional differential equations  
Numerical solution for multi-dimensional Riesz fractional nonlinear reaction–diffusion equation by exponential Runge–Kutta method Journal article
Journal of Applied Mathematics and Computing, 2020,Volume: 62,Issue: 1-2,Page: 449-472
Authors:  Zhang,Lu;  Sun,Hai Wei
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Exponential Runge–Kutta method  Matrix exponential  Riesz fractional reaction–diffusion equation  Shift-invert Lanczos method  Toeplitz structure