Solution to strongly nonlinear parabolic problems by a linear approximation scheme

A nonlinear parabolic problem is solved by a linear approximation scheme using a nonstandard time discretization with a relaxation function. The relaxation function is determined by iterations. Optimal rate of convergence is proved for semi-discretization (in time). Error estimates are obtained for the full discretization scheme (in time and space). The proposed approximation scheme converges also in the case of degenerate parabolic problems.