Abstract
In this paper, a meshless numerical algorithm is developed for the solution of two-dimensional diffusion equations with different boundary conditions. The proposed numerical method, which is truly meshless and quadrature-free, is based on the time-marching finite difference scheme, the method of the particular solutions and the singular boundary method. The diffusion equation is transformed into a Poisson-type or a modified Helmholtz equation after the time domain is discretized by the Euler or Houbolt finite difference scheme.
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