為了解決物理問題中面臨偏微分方程式之求解，各式計算方法於焉產生。本文之微分再生核內插法，將內插函數分為原始函數與改善函數，其中原始函數滿足Kronecker delta性質，而改善函數則是由一組微分再生核條件求得。用此方法則能很容易的代入幾何邊界條件。不同於傳統RK (reproducing kernel)法直接對形狀函數微分求取高階形狀函數，而本法係建立一組微分再生核條件來求得高階形狀函數。本文呈現之數值範例能展現DRK內插法之分析能有很好的精度與快速之收歛性。

A meshfree collocation method based on the differential reproducing kernel (DRK) interpolation is proposed for solving partial differential equations governing a certain physical problem. A general formulation for the present DRK interpolation method is developed. The interpolation function at each referred node is separated into a primitive function processing Kronecker delta properties and an enrichment function constituting reproducing conditions. By means of the present DRK interpolation, the essential boundary conditions can be readily applied, exactly like the implementation in finite element methods. Contrary to the manipulation in conventional reproducing kernel (RK) methods where the differential operation towards the shape functions of the RK approximants is directly taken, we construct a set of differential reproducing conditions to determine the shape functions for the derivatives of DRK interpolants. A point collocation method based on the present DRK interpolation for the deformation and stress analyses of several one- and two-dimensional elastic solids is illustrated. It is shown that the present DRK interpolation-based collocation method indeed is a fully meshfree approach with excellent accuracy and fast rate of convergence.

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