Abstract: By the theory of generalized functions this paper introduces a specific generalized function, by which, together with its various derivatives, the boundary integral equations and its arbitrary derivatives of any sufficiently smooth function can be established. These equations have no non-integral singularities. For a problem defined by linear partial differential operators, the partial differential equations of the problem can always be converted into boundary integral equations so long as the relevant fundamental solutions exist.

Key words: numerical solution, induced magnetic field, magnetohydrodynamic (MHD) flow, boundary layer, heat transfer, stretching sheet