Abstract: The elliptic type equation-Δu+k²u=f (1) is derived from heat conduction equation by finit difference discreting. The ordinary boundary integral equation of (1) is of the second kind for the unknown potential, but is the first kind for the unknown exterior normal derivative of potential. In this paper, a new type of boundary integral equation has been derived by conservation integral method, which is of the second kind for the unknown exterior normal derivative of potential and is the frist kind for the unknown poential, and the two equations method for the mixed boundary value prblem of (1) is presented, which use the ordinary boundary integral equation at the collocation points in the boundary segment in which the potential is unknown, and use the new type of boundary integral equation at the collocation points in the boundary segment in which the exterior normal derivative is unknown. Some numerical examples indicate this method has higer accuracy than ordinary boundary element method.

Key words: boundary integral equation, heat conduction, double equations method