在本篇論文中，我們利用純量輔助變量法去模擬福克-普朗克方程式，純量輔助變量法用於修改與系統相關的能量，使其在離散水平上單調遞減，為梯度流模型構造出一個無條件能量穩定的數值方案，由此產生的數值方案是高效且易於實施的。我們對此數值方案採用二階有限差分法對空間作離散化，時間上使用前向歐拉法獲得顯式方案。在數值實驗方面，我們得到了預期的收斂階數，並比較在不同時間步長下修改前後能量的差異，我們還證明了在此數值結構下仍保持質量守恆和能量耗散這兩種性質

In this paper, we apply the scalar auxiliary variable method to simulate the Fokker-Planck equation. The SAV method is used to modify the free energy associated with the system such that it decreases monotonically at the discrete level to construct an unconditionally energy stable numerical scheme for the gradient flow model, the resulting numerical scheme is efficient and easy to implement. For this numerical scheme, we use the second-order finite difference method to discretize the space, and use the forward Euler method to obtain an explicit scheme in time. In numerical experiments, we obtain the expected order of convergence and compare the difference between the modified and original energy at different time steps, we also prove that both properties of mass conservation and energy dissipation are preserved under this numerical structure

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