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The study aims to develop a time-space two-grid compact difference method for solving the nonlinear Schrödinger equation efficiently.

April 11, 2026AxiomsOpen Access

An Efficient Time-Space Two-Grid Compact Difference Method for the Nonlinear Schrödinger Equation: Analysis and Simulation

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Novel method improves computational efficiency in solving nonlinear Schrödinger equation, suggesting a promising alternative in numerical analysis.

The study aims to develop a time-space two-grid compact difference method for solving the nonlinear Schrödinger equation efficiently.
Introduced a high-order compact difference scheme with a coarse and fine grid approach.
Applied both nonlinear and linearized correction algorithms to enhance efficiency.
Proven unconditional stability and optimal convergence rates using energy methods and a discrete Sobolev inequality.
Conducted numerical experiments to validate theoretical results.
Achieved fourth-order convergence in space and second-order in time without grid ratio constraints.
Demonstrated significant CPU time reduction compared to fully nonlinear schemes with similar accuracy.
Validated robustness through single and two-soliton simulations.

Bai et al. (2026) studied this question.

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Novel method improves computational efficiency in solving nonlinear Schrödinger equation, suggesting a promising alternative in numerical analysis.