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The Residual Smooting Scheme (RSS) have been introduced in\cite{AverbuchCohenIsraeli} as a backward Euler's method with a simplifiedimplicit part for the solution of parabolic problems. RSS have stabilityproperties comparable to those of semi-implicit schemes while givingpossibilities for reducing the computational cost. A similar approach wasintroduced independently in \cite{BCostaPHD,CDGT} but from the Fourier point ofview. We present here a unified framework for these schemes and proposepractical implementations and extensions of the RSS schemes for the long timesimulation of nonlinear parabolic problems when discretized by using high orderfinite differences compact schemes. Stability results are presented in thelinear and the nonlinear case. Numerical simulations of 2D incompressibleNavier-Stokes equations are given for illustrating the robustness of themethod.

Stabilized Times Schemes for High Accurate Finite Differences Solutions of Nonlinear Parabolic Equations