Mathematical Methods in the Applied Sciences· 2026Q2
A Class of Arbitrarily High‐Order Energy‐Conserving Schemes for the Nonlinear Schrödinger Wave Equation
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- Q2SCImago
- 2026year
Short summary
Researchers developed arbitrarily high-order energy-conserving numerical schemes for the nonlinear Schrödinger wave equation, overcoming limitations of existing methods that either lose energy conservation or have low temporal accuracy.
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Key points
- Proposes arbitrarily high-order energy-conserving numerical schemes for the nonlinear Schrödinger wave equation.
- Combines compact difference for spatial and Petrov-Galerkin for temporal discretization.
- Rigorously proves the discrete energy conservation law theoretically.
- Develops an efficient linearized fixed-point iteration algorithm for implicit schemes.
- Numerically demonstrates superior computational efficiency compared to existing high-order schemes.
AI-generated from the title and abstract; the full text is not read.
Abstract
ABSTRACT This article proposes a class of arbitrarily high‐order energy‐conserving schemes for the nonlinear Schrödinger wave equation, aiming to address the issue that existing conservative schemes generally either fail to preserve the original energy conservation property or suffer from low temporal accuracy. The compact difference method is employed for spatial discretization and the Petrov–Galerkin (PG) method for temporal discretization, thereby constructing a fully discrete numerical scheme. At the theoretical level, the discrete energy conservation law of the scheme is rigorously proven. Furthermore, an efficient linearized point‐wise fixed‐point iteration algorithm is developed to achieve fast solving of the derived implicit schemes. Numerically, a series of numerical experiments is carried out to verify the theoretical results and demonstrate that the proposed schemes outperform the existing temporal high‐order original energy‐conserving schemes in computational efficiency.
The authors' abstract, as published at the source. Mathematical Methods in the Applied Sciences, 2026 · DOI ↗
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Field: Numerical Analysis
Numerical AnalysisMathematics