The important disadvantage of BEM is that when an interior point is much closer to the boundary of the domain, great errors occurs due to the Green's function in the BEM formulation. In order to overcome this disadvantage, integration by parts is applied to the boundary element formulation in complex plane, then a new BEM formulation is obtained based on 2nd kind Green's function that is defined as a new function by the integration by parts. Also new flux formulations for the interior points are obtained by using this new BEM formulation based on 2nd kind Green's function. When this new interior BEM formulation and new flux formulations are used, errors decreased for the interior points especially when this points are getting much closer to the boundary. A sample problem is analyzed with BEM and also with new approached BEM and its solutions are compared to those obtained analytically. Comparisons show that new approached interior formulation and flux formulations behave much better and reduce errors for the interior points closer to the boundary.
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