4.1.3 Nonlinear Equation Solution

  After discretization of the diffusion equations we have a system of nonlinear algebraic equations. The diffusion equations are discretized for every solution variable x, mostly dopant concentrations, on every grid node. This leads to an equation system of rank , the number of unknown quantities times the number of grid points . The discretized equations are represented by vector functions for each grid node.

 

Since the system is nonlinear, only iterative methods are applicable for the solution.

• Newton-Iteration Method