A novel method to solve 2nd order neumann type boundary value problems in electrostatics

Abstract

In this paper, the numerical method of nonpolynomial spline approximation is used to solve 2nd order Neumann type boundary value problems (bvp's) in electrostatics. This new approach provides more accurate results than the polynomial approximations and the spectral methods. The literature contains very little on the solution of Neumann type bvp's because of the fact that a unique solution does not exist for all problems. In electrostatics, Neumann type bvp's are encountered for finding the electrostatic potential inside closed surfaces where the normal derivative of the electric potential is specified everywhere on the surface. Two examples are presented to prove the accuracy of the proposed method. In these examples, the governing differential equation is solved to find the electrostatic potential inside a region bounded by conductors that are maintained at constant voltages. The results are compared with the analytic solutions.