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Implicit-explicit time discretization with complex time for parabolic equations
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DOI：10.1016/j.cnsns.2026.109743.png)
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• Novel high-order construction and efficiency: We propose an arbitrary-order Implicit-Explicit (IMEX) time discretization framework based on the complex time plane, which circumvents the complexity of traditional high-order scheme construction. The method utilizes a decoupled algebraic structure that permits efficient vectorized operations, yielding superior computational efficiency over explicit Runge-Kutta methods without compromising stability. • Unified stability and convergence theory: We provide a unified characterization of stability regions for ODEs and PDEs, proving that the scheme’s stability region is identical to that of explicit Runge-Kutta methods and coincides with its absolute stability region. Furthermore, we rigorously establish the scheme’s L2-stability and arbitrary-order convergence. • Robustness in nonlinear phase-field modeling: The proposed method is validated through stiff nonlinear phase-field models, specifically the Allen-Cahn and Cahn-Hilliard equations. Results confirm the scheme preserves essential physical properties, including energy dissipation and mass conservation, while achieving high-order accuracy in multidimensional settings.
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3.8
论文数:
9.3K
被引数:
1.8W
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