Finite Difference Methods for the First Boundary Value Problem of Δu(x,y)=r(x,y,u) and Curved Boundaries

摘要

It can be shown, that we get formulas causing only a small increase of labor in comparison to those for regular grid points. If furtheron r(x.y.u) depends only linearly on u, it becomes clear, that the Mehrstellen method brings a small increase of labor only, does not increase the number of computing points – that is unknown quantities – and still yields a considerable increase of accuracy.