Equilibrium attractivity of Krylov-W-methods for nonlinear stiff ODEs

Since implicit integration schemes for differential equations which use Krylov methods for the approximate solution of linear systems depend nonlinearly on the actual solution a classical stability analysis is difficult to perform. A different, weaker property of autonomous dissipative systemsy′=f(y) is that the norm ‖f(y(t))‖ decreases for any solutiony(t). This property can also be analysed for W-methods using a Krylov-Arnoldi approximation. We discuss different additional assumptions onf and conditions on the Arnoldi process that imply this kind of attractivity to equilibrium points for the numerical solution. One assumption is general enough to cover quasilinear parabolic problems.

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