Equivalence Between Convergence and Stability of General Nonlinear Difference Schemes

摘要

An extension to the nonlinear version for the Lax-Richtmyer equivalence between the convergence and stability of linear difference schemes that are consistent with properly posed linear evolution partial differential equations is discussed. It extended in order to accommodate the solutions of nonlinear evolution partial differential equations exhibiting finite 'blow-up' time, which may depend on initial and/or boundary value conditions.