Using increment-dimensional precise integration method for solving transient heat conduction problems discretized by the MLPG method

In this paper, a novel numerical method is proposed to solve two-dimensional transient heat conduction problems. The space domain is discretized with an improved MLPG method, which has combined the advantages of natural neighbour interpolation and Petrov-Galerkin (MLPG) method. The semi discrete heat conduction equation is solved in the time domain with increment-dimensional precise integration method. The numerical results show that the present solution procedure is effective and accurate.