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Your search keyword '"Ding, Hengfei"' showing total 2 results
2 results on '"Ding, Hengfei"'

1. Structure preserving fourth-order difference scheme for the nonlinear spatial fractional Schrödinger equation in two dimensions.

Author

Ding, Hengfei and Tian, Junhong

Subjects
*CRANK-nicolson method, *NUMERICAL analysis, *SCHRODINGER equation, *GENERATING functions
Abstract

In this paper, we focus on develop high-order and structure-preserving numerical algorithm for the two-dimensional nonlinear space fractional Schrödinger equations. By constructing a new generating function, we obtain a fourth-order numerical differential formula and use it to approximate the spatial Riesz derivative, while the Crank–Nicolson method is applied for the time derivative. Based on the energy method, the conservation, solvability and convergence of the numerical algorithm are proved. Finally, some numerical examples are used to verify the correctness of the theoretical analysis and the validity of the numerical algorithm. [ABSTRACT FROM AUTHOR]

Published
2023
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2. Numerical analysis of the high-order scheme of the damped nonlinear space fraction Schrödinger equation.

Author

Ding, Hengfei and Li, Changpin

Subjects
*NUMERICAL analysis, *ORDINARY differential equations, *NONLINEAR differential equations, *SCHRODINGER equation, *FRACTIONS
Abstract

Firstly, we construct a fourth-order numerical differential formula for approximating Riesz derivative. Substituting it into the damped nonlinear space fractional Schrödinger equation, the original equation becomes a matrix form of nonlinear ordinary differential equation system. Then, by means of implicit integrating factor method and Padé approximation, we obtain a new numerical scheme whose convergence order is higher than the existing algorithms. Finally, a numerical example is given to verify the effectiveness of the numerical algorithm and the correctness of the theoretical analysis. [ABSTRACT FROM AUTHOR]

Published
2023
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