The application of homotopy perturbation method (HPM) for solving systems of linear equations is further discussed and focused on a method for choosing an auxiliary matrix to improve the rate of convergence. Moreover, solving of convection-diffusion equations has been developed by HPM and the convergence properties of the proposed method have been analyzed in detail; the obtained results are compared with some other methods in the frame of HPM. Numerical experiment shows a good improvement on the convergence rate and the efficiency of this method.
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