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The convergence of a family of AMF-Runge-Kutta methods (in short AMF-RK) forthe time integration of evolutionary Partial Differential Equations (PDEs) ofAdvection Diffusion Reaction type semi-discretized in space is considered. Themethods are based on very few inexact Newton Iterations of Aproximate MatrixFactorization splitting-type (AMF) applied to the Implicit Runge-Kuttaformulas, which allows very cheap and inexact implementations of the underlyingRunge-Kutta formula. Particular AMF-RK methods based on Radau IIA formulas areconsidered. These methods have given very competitive results when comparedwith important formulas in the literature for multidimensional systems ofnon-linear parabolic PDE problems. Uniform bounds for the global time-spaceerrors on semi-linear PDEs when simultaneously the time step-size and thespatial grid resolution tend to zero are derived. Numerical illustrationssupporting the theory are presented.

Error estimates for splitting methods based on AMF-Runge-Kutta formulas for the time integration of advection diffusion reaction PDEs