Numerical analysis of the high-order scheme of the damped nonlinear space fraction Schrödinger equation

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 i...

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Bibliographic Details
Published in:Applied mathematics letters 2023-07, Vol.141, p.108621, Article 108621
Main Authors: Ding, Hengfei, Li, Changpin
Format: Article
Language:English
Subjects:
Numerical differential formula
Riesz derivative
The damped nonlinear space fractional Schrödinger equations
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Summary: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.
ISSN:0893-9659
1873-5452
DOI:10.1016/j.aml.2023.108621