13 Result(s)
within
**-Wei Sun
Mathematics
Computational Mathematics and Numerical Analysis
Theoretical, Mathematical and Computational Physics
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Article
Optimal Error Estimates of SAV Crank–Nicolson Finite Element Method for the Coupled Nonlinear Schrödinger Equation
In this paper, we reformulate the coupled nonlinear Schrödinger (CNLS) equation by using the scalar auxiliary variable (SAV) approach and solve the resulting system by using Crank-Nicolson finite element metho...
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Article
Preconditioning Technique Based on Sine Transformation for Nonlocal Helmholtz Equations with Fractional Laplacian
We propose two preconditioners based on the fast sine transformation for solving linear systems with ill-conditioned multilevel Toeplitz structure. These matrices are generated by discretizing the two-dimensio...
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Article
Numerical Study of a Fast Two-Level Strang Splitting Method for Spatial Fractional Allen–Cahn Equations
In this paper, a numerical method to solve the multi-dimensional spatial fractional Allen–Cahn equations has been investigated. After semi-discretizating the equations, a system of nonlinear ordinary different...
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Article
A Sixth-Order Quasi-Compact Difference Scheme for Multidimensional Poisson Equations Without Derivatives of Source Term
Sixth-order compact difference schemes for Poisson equations have been widely investigated in the literature. Nevertheless, those methods are all constructed based on knowing the exact values of the derivative...
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Article
Preconditioners with Symmetrized Techniques for Space Fractional Cahn-Hilliard Equations
In this paper, we study space fractional Cahn-Hilliard equations. A second-order stabilized finite difference scheme is exploited for the model equations. The resulting coefficient matrix is a nonsymmetric ill...
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Article
A Novel Discrete Fractional Grönwall-Type Inequality and Its Application in Pointwise-in-Time Error Estimates
We present a family of fully-discrete schemes for numerically solving nonlinear sub-diffusion equations, taking the weak regularity of the exact solutions into account. Using a novel discrete fractional Grönwa...
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Article
A Dimensional Splitting Exponential Time Differencing Scheme for Multidimensional Fractional Allen-Cahn Equations
This paper is concerned with numerical methods for solving the multidimensional Allen-Cahn equations with spatial fractional Riesz derivatives. A fully discrete numerical scheme is proposed using a dimensional...
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Article
A Fast Algorithm for the Variable-Order Spatial Fractional Advection-Diffusion Equation
We propose a fast algorithm for the variable-order (VO) space-fractional advection-diffusion equations with nonlinear source terms on a finite domain. Due to the impact of the space-dependent the VO, the resul...
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Article
Stochastic Variance Reduced Gradient Methods Using a Trust-Region-Like Scheme
Stochastic variance reduced gradient (SVRG) methods are important approaches to minimize the average of a large number of cost functions frequently arising in machine learning and many other applications. In t...
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Article
Exponential Runge–Kutta Method for Two-Dimensional Nonlinear Fractional Complex Ginzburg–Landau Equations
In this work, we study numerically two-dimensional nonlinear spatial fractional complex Ginzburg–Landau equations. A centered finite difference method is exploited to discretize the spatial variables and leads...
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Article
Stability and Convergence Analysis of Finite Difference Schemes for Time-Dependent Space-Fractional Diffusion Equations with Variable Diffusion Coefficients
In this paper, we study and analyze Crank–Nicolson temporal discretization with high-order spatial difference schemes for time-dependent Riesz space-fractional diffusion equations with variable diffusion coeff...
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Article
Fast Laplace Transform Methods for Free-Boundary Problems of Fractional Diffusion Equations
In this paper we develop a fast Laplace transform method for solving a class of free-boundary fractional diffusion equations arising in the American option pricing. Instead of using the time-step** methods, ...
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Article
Fast Numerical Contour Integral Method for Fractional Diffusion Equations
The numerical contour integral method with hyperbolic contour is exploited to solve space-fractional diffusion equations. By making use of the Toeplitz-like structure of spatial discretized matrices and the re...
