Convergence of Runge-Kutta methods for nonlinear parabolic equations

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Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review (2016, methodology): “Ostermann and Thalhammer [329] study strongly A(α)-stable methods applied to parabolic nonlinear equations and obtain convergence rates of Min(p, q+1) independent of whether the step-size was fixed or not.”