本文首先發展拉格朗日微分再生核內插適點法，每個節點的形狀函數被分離成初始函數和修正函數，使用一組再生條件決定每個節點處之初始函數與一個簡單的歸一化核函數涵蓋了所有的鄰近點，並將之指定為形狀函數，採用每個節點影響半徑內不包含任何鄰近點之四次平滑函數作為修正函數且滿足Kronecker Delta性質。隨後，每個節點的微分再生核內插函數之形狀函數導數由使用一組微分再生條件導出的初始函數和修正函數之導數所決定。接下來發展赫麥特微分再生核內插適點法，梁與平板控制方程式為四階微分方程，並且在幾何邊界條件中與橫向撓度 與其對空間座標一次導數得到之斜率有關，此法將撓度與轉角同時視為主變數且赫麥特函數滿足Kronecker Delta性質以方便施加幾何邊界條件，上述方法均與文獻理論解作比較，以驗證其準確性和探討收斂速率。

The present paper first develops the Lagrange differential reproducing kernel (DRK) interpolation-based collocation method the differential reproducing kernel interpolation method. The novelty of this method is that we construct a set of differential reproducing conditions to determine the shape functions of derivatives of the DRK interpolation function, without directly differentiating the DRK interpolation function. In addition, the shape function of the DRK interpolation function at each collocation node is separated into a primitive function constituting reproducing conditions and an enrichment function processing Kronecker delta properties, so that the nodal interpolation properties are satisfied. The Hermite DRK interpolation method is developed later for solving fourth-order differential equations where the field variable and its first-order derivatives are regarded as the primary variables that the nodal interpolation properties are satisfied for the field variable and its first-order derivatives. These methods are compared with the literature theory solution to verify its accuracy and to discuss the convergence rate.

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