R69-8 Hybrid Computer Integration of Partial Differential Equations by Use of an Assumed Sum Separation of Variables

The problem posed in this paper is the solution of Laplace´s equation using the cylindrical coordinates r and z in an axially symmetric region. The boundary for this region consists of the surface r=b(z) and two end planes at z=0 and z=a. Assuming that the potential is specified on this boundary, the solution for V(r, z) is desired for all interior points. An example of an application is the design of an electron gun in which the solution for the electrostatic potential is used in computing electron trajectories.