| Abstract: |
| Developing efficient numerical algorithms for highly nonlinear and coupled Partial Differential Equation (PDE) systems has been a longstanding challenge, prompting numerous efforts in this field over many years. We aim to construct a framework approach to address major weaknesses in nearly all existing numerical algorithms designed for solving coupled nonlinear gradient flow systems. These methods have been applied to some well-known systems, such as the anisotropic phase-field dendritic crystal growth model, yielding efficient numerical schemes characterized by linearity, a fully decoupled structure, unconditional energy stability, and second-order time accuracy. These features showcase the algorithms` considerable potential for practical applications. |
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