In this chapter, we will show how the coupled system of non-linear partial differential equations, projected on a discrete mesh, is linearized, and introduce some of the many numerical methods to solve the resulting system of linear equations. The methods presented here are not complete by far. This would in any event not fit into the framework of the intention of this book. We show how the solution is performed in principle, and present a few methods selected from the daily praxis, to give a glimpse on the non-trivial numerical algorithms in a device simulator. In addition, we briefly discuss some possible improvements of its performance.
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