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| Study on point collocated meshless method based on reproducing kernel ideas for one-dimensional problems |
| Revised:May 13, 2002 |
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| DOI：10.7511/jslx20041020 |
| KeyWord:meshless method,reproducing kernel particle method,point collocation method |
| Shi Baojun~ |
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| Abstract: |
| Meshless method can be mainly divided into, according its discretizing principle, two kinds of type: Galerkin-type and point collocated-type. The implementation of Galerkin meshless method needs a background mesh. So it is not a true meshless method. While the point collocated meshless method is a real meshless method because its implementation does not need any background mesh. The basic principle of reproducing kernel particle method was first introduced in this paper. Then a new point collocated meshless method for one-dimensional problem was presented based on the reproducing kernel ideas combined with the point collocation method. The calculation of the approximation function and its derivatives, that of the correction function and its implementation were investigated. Numevical examples are given to show the accuracy and convergence of the proposed method. |
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