Mathematical Models for Nano Science - Politecnico di Milano

Numerical Approach
Rothe method
• Fully coupled system
• Strongly nonlinear equations
• Time discretization with Runge-Kutta methods
• Linearization of the problems
• Spatial discretization
Functional iteration algorithms
• Newton method: faster convergence but less robust.
• Gummel map: staggered algorithm, (possibly) slower but
robust. Also useful as a solution map for the analysis of
existence/uniqueness.