Energy-Preserving Algorithms for the Ginzburg–Landau Equation: Integrating Scientific Research with Talent Cultivation

This study proposes a novel structure-preserving algorithm for the Ginzburg–Landau equation (GLE) by combining the Fourier pseudospectral method with the Exponential Average Vector Field (EAVF) scheme. The proposed numerical framework strictly preserves the energy dissipation property of GLE systems, as validated through theoretical analysis and numerical experiments on solitary wave dynamics. Compared to conventional methods such as the average vector field approach, the EAVF-based scheme demonstrates superior computational efficiency, including faster convergence and enhanced stability under larger time steps, enabling accurate long-term simulation of strongly nonlinear GLE systems. Furthermore, this research incorporates a pedagogical innovation through its implementation within an undergraduate innovation project. By adopting a “problem decomposition–code verification–modular development” training model, students engage in the full cycle of algorithm design, implementation, and validation. This practice-oriented approach significantly enhances students’ competencies in scientific programming, complex problem-solving, and research-oriented thinking, providing an effective paradigm for synergizing advanced computational research with talent cultivation in STEM education.