The paper shows how the method of separation of variables, digital computation and Fourier synthesis may be combined to give the approximate solution of a particular field problem. The problem concerns the fringing flux at the tip of a cylindrical permeable magnetic pole face. Selected co-ordinate surfaces subdivide the volume of the field into regions within which the scalar potential may be expressed by Fourier expansions with unknown coefficients. A set of simultaneous equations for solution in these coefficients by digital computer is derived by satisfying continuity at chosen points which lie on the interfaces separating the several regions. The exact solution is approached by increasing the number of interface points.