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: We study the convergence properties of implicit Runge-Kutta methods appliedto time discretization of parabolic equations with timeor solution-dependent operator.Error bounds are derived in the energy norm. The convergence analysis uses two differentapproaches. The first, technically simpler approach relies on energy estimates and requiresalgebraic stability of the Runge-Kutta method. The second one is based on estimates forlinear time-invariant equations and uses Fourier and...

Runge-Kutta Approximation of Quasi-Linear Parabolic Equations