A Noniterative Numerical Solution of Poisson’s and Laplace’s Equations With Applications to Slow Viscous Flow

Abstract

A noniterative finite-difference method for solution of Poisson’s and Laplace’s equations for linear boundary conditions is given. The method is simpler and more accurate than iterative procedures. It is limited in the number of meshes that can be used, but that number is adequate to obtain accurate solutions to many engineering problems. The computational effort is reduced vastly when one differential equation must be solved in a family of domains for the same boundary condition. The same applies to calculations of the integral of the function in the domain. Examples are given for simultaneous solution in Laplace’s and Poisson’s equations and for problems with multiple boundary conditions. The results of several slow viscous-flow problems are discussed.