Study on point collocated meshless method based on reproducing kernel ideas for one-dimensional problems

Meshless method can be mainly divided into, according its discretizing principle, two kinds of type: Galcrkin-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 calculations of the approximation function and its derivatives, the correction function and its implementation are investigated. Numerical examples are given to show the accuracy and convergence of the proposed method.EI0197-1032