Abstract: The high-order boundary conditions for the problems cf Laplace equation in infinite region have been developed.The improvement in accuracy for numerical solution is achieved by imposing the high-order boundary conditions on the exterior boundarv of a reduced finite region in which the numerical method is used.So both the computing efforts and the required storage in computer are reduced.The numerical examples show that the 1st-order boundary condition approaches to the exact boundary condition and it is clearly superior to the traditional boundary condition and the 2nd-order boundary condition.

Key words: Laplace equation, potential function, boundary condition, conformal transformation