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- Title
A High-Order L1-2 Scheme Based on Compact Finite Difference Method for the Nonlinear Time-Fractional Schrodinger Equation.
- Authors
Yuting Zhang; Lingzhi Qian
- Abstract
In this paper, a high-order L1-2 scheme based on the compact finite difference method for the nonlinear timefractional Schrodinger equation with homogeneous Dirichlet ¨ boundary condition is derived. Firstly, a standard fully discrete numerical scheme is constructed by adopting the L1-2 formula to approximate the Caputo fractional derivative for the time discretization and the compact finite difference method for the space discretization. In addition to proving the unique solvability of the numerical solution, we also established the convergence analysis of the fully discrete numerical scheme based on the discrete Gronwall inequality. Furthermore, the ¨ global convergence order O(τ3−α+h4 ) in discrete L² -norm of the numerical scheme is proved rigorously. A variety of numerical results are carried out to confirm the theoretical analysis.
- Subjects
FINITE difference method; SCHRODINGER equation; FINITE differences; CAPUTO fractional derivatives; GRONWALL inequalities; DISCRETIZATION methods
- Publication
Engineering Letters, 2023, Vol 31, Issue 4, p1592
- ISSN
1816-093X
- Publication type
Article