Shih-Wei Yang1, Yung-Ming Wang1, Chih-Ping Wu1,2, Hsuan-Teh Hu1
CMES-Computer Modeling in Engineering & Sciences, Vol.60, No.1, pp. 1-40, 2010, DOI:10.3970/cmes.2010.060.001
Abstract A differential reproducing kernel (DRK) approximation-based collocation method is developed for solving ordinary and partial differential equations governing the one- and two-dimensional problems of elastic bodies, respectively. In the conventional reproducing kernel (RK) approximation, the shape functions for the derivatives of RK approximants are determined by directly differentiating the RK approximants, and this is very time-consuming, especially for the calculations of their higher-order derivatives. Contrary to the previous differentiation manipulation, we construct a set of differential reproducing conditions to determine the shape functions for the derivatives of RK approximants. A meshless collocation method based on the present DRK approximation is… More >
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