DUAL SERIES EQUATIONS TO SOLVE THE LAPLACE EQUATION WITH MIXED BOUNDARY CONDITIONS

A solution of the Laplace equation in cylindrical coordinates is presented for a bounded cylinder with the known height and radius which is subject to inhomogeneous mixed boundary conditions of the third and second kinds on the surface. On the other surface, unmixed boundary conditions of the fi rst or second kind are given. Through separation of variables, the Hankel integral transform, and the dual series equations, the solution of the mixed problem is reduced to solving the Fredholm integral equation of the second kind
A solution of the Laplace equation in cylindrical coordinates is presented for a bounded cylinder with the known height and radius which is subject to inhomogeneous mixed boundary conditions of the third and second kinds on the surface. On the other surface, unmixed boundary conditions of the fi rst or second kind are given. Through separation of variables, the Hankel integral transform, and the dual series equations, the solution of the mixed problem is reduced to solving the Fredholm integral equation of the second kind
Author:  N. A. Hoshan
Keywords:  dual series equations, mixed boundary conditions
Page:  1460