A technique combined the Rothe method with two-grid (coarse and fine) algorithm of Xu for computation of numerical solutions of nonlinear parabolic problems with various boundary conditions is presented. For blow-up solutions we use a decreasing variable step in time, according to the growth of the solution. We give theoretical results, concerning convergence of the numerical solutions to the analytical ones. Numerical experiments for comparison the accuracy of the algorithm with other known numerical schemes are discussed.
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