Gap in Nonlinear Equivalence for Numerical Methods for PDEs

Details Gap in Nonlinear Equivalence for Numerical Methods for PDEs Gap in Nonlinear Equivalence for Numerical Methods for PDEs

2008-06-27

arxiv.org/abs/0806.4491v2

Mathematics

General Mathematics

Scientific paper

For a large class of nonlinear evolution PDEs, and more generally, of nonlinear semigroups, as well as their approximating numerical methods, two rather natural stability type convergence conditions are given, one being necessary, while the other is sufficient. The gap between these two stability conditions is analyzed, thus leading to a general nonlinear equivalence between stability and convergence.

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