Abstract

In Meshless natura1 neighbour Petrov-Galerkin method, The natural neighbour interpolation is used as trial function and
a weak form over the local polygonal sub-domains constructed by Delaunay triangular is used to obtain the discretized
system of equilibrium equations, and it’s a new truly meshless method. This method simplified the formation of the
equilibrium equations, facilitates the imposition of essential boundary conditions and the system stiffness matrix in the
present method is banded and sparse. Efforts are made to study Meshless natural neighbour Pettrov-Galerkin Method,
which is extended to solve the transient heat conduction. The numerical results show that the present method is quite
accurate and stable.

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