28 Result(s)
within
**-Wei Sun
Mathematics
Computational Mathematics and Numerical Analysis
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Article
Sixth-order quasi-compact difference scheme for the time-dependent diffusion equation
This paper focuses on develo** a numerical method with high-order accuracy for solving the time-dependent diffusion equation. We discrete time first, which results in a modified Helmholtz equation at each ti...
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Article
Asymptotical stability of the exact solutions and the numerical solutions for impulsive neutral differential equations
In this paper, we not only study asymptotical stability of a class of linear impulsive neutral delay differential equations(INDDEs), but also study stability and asymptotical stability of nonlinear INDDEs. Asy...
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Article
An efficient red–black skewed extrapolation cascadic multigrid method for two-dimensional Poisson equation
We present a red–black skewed extrapolation cascadic multigrid (SkECMG) method to solve the Poisson equation in two dimensions based on the modified standard and skewed five-point finite difference discretizat...
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Article
Efficient finite difference scheme for a hidden-memory variable-order time-fractional diffusion equation
In this paper, a fast and memory-saving numerical scheme is presented for solving hidden-memory variable-order time-fractional diffusion equations based on the L1 method. Due to the nonlocality of fractional o...
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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
Exponential-sum-approximation technique for variable-order time-fractional diffusion equations
In this paper, we study the variable-order (VO) time-fractional diffusion equations. For a VO function \(\alpha (t)\in (0,1)\) ...
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Article
Splitting preconditioning based on sine transform for time-dependent Riesz space fractional diffusion equations
We study the sine-transform-based splitting preconditioning technique for the linear systems arising in the numerical discretization of time-dependent one dimensional and two dimensional Riesz space fractional...
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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
Numerical solution for multi-dimensional Riesz fractional nonlinear reaction–diffusion equation by exponential Runge–Kutta method
A spatial discretization of the Riesz fractional nonlinear reaction–diffusion equation by the fractional centered difference scheme leads to a system of ordinary differential equations, in which the resulting ...
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Article
Balanced \(2^k\) -variable rotation symmetric Boolean functions with optimal algebraic immunity
Rotation symmetric Boolean functions have been extensive studied because of their importance in cryptography. These functions are invariant under circular translation of indices. In this paper, we propose a ne...
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Article
Generalized inverse eigenvalue problems for augmented periodic Jacobi Matrices
In this paper, we propose a new method to solve the generalized inverse eigenvalue problem for periodic Jacobi matrices. Besides, we introduce a new inverse eigenvalue problem for augmented periodic Jacobi mat...
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Article
A preconditioned fast finite difference scheme for space-fractional diffusion equations in convex domains
A fast finite difference method is developed for solving space-fractional diffusion equations with variable coefficient in convex domains using a volume penalization approach. The resulting coefficient matrix ...
