document: Convergence of Runge-Kutta methods for nonlinear parabolic equations We study time discretizations of fully nonlinear parabolic differential equations . Our analysis uses the fact that the linearization along the exact solution is a uniformly sectorial operator . We derive smooth and nonsmooth-data error estimates for the backward Euler method , and we prove convergence for strongly A -LRB- v -RRB- - stable Runge-Kutta methods . For the latter , the order of convergence for smooth solutions is essentially determined by the stage order of the method . Numerical examples illustrating the convergence estimates are presented
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extractive_keyphrases: time discretizations linearization uniformly sectorial operator backward euler method nonlinear parabolic differential equations
abstractive_keyphrases: runge-kutta method convergence nonsmooth-data error estimates data error estimates