Difference schemes for a quasi-linear parabolic equation with various boundary conditions are considered. A method for studying the convergence of approximate solutions and their derivatives is proposed. Estimates of the rate of convergence for solutions and derivatives up to certain orders of magnitude are derived. It is shown that all estimates obtained by this method are definitive for the boundary value problems under study in the bounded domain under consideration.

quasi-linear parabolic equation, difference method, convergence rate, accuracy

Mathematical problems and theory of numerical methods