Abstract
In this paper, the three boundary value problems on Poisson's problem are analyzed by using a new meshless method that is called the over-range collocation method (ORCM). By introducing some collocation points, which are located at outside of domain of the analyzed body, unsatisfactory issue of the positivity conditions of boundary points can be avoided. Convergence studies in the numerical examples show that the ORCM possesses good convergence for both the unknown variables and their derivatives. Quite accurate numerical results calculated by both regular nodal models and irregular nodal models have been obtained.
