Relaxation procedure for calculation of potential distribution in nonlinear dielectrics

A relaxation procedure for the numerical solution of any two-dimensional potential distribution in nonlinear polar dielectrics with Dirichlet boundary conditions is proposed. Using the differential equation for the potential in a nonlinear polar dielectric, the corresponding difference equation is obtained. This difference equation is the basis of the relaxation procedure outlined. An example is analysed and the potential distributions for the linear and nonlinear situations are compared, showing the effect of nonlinearity.