Finite Difference Methods for Elliptic Equations

In this chapter we discuss numerical methods for solving elliptic equations, such as Poisson’s equation or the Grad-Shafranov equation. A general mathematical classification of equation types as elliptic, parabolic, or hyperbolic can be found elsewhere [26, 29]. Elliptic equations need boundary conditions of either the Dirichlet or Neumann type specified on a closed surface to possess unique solutions.